Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Webpage for Mathematical Logic
Important Question Types:
Checking validity of First Order Logic Statements
Checking validity of Propositional Logic
Recent questions tagged mathematical-logic
0
votes
0
answers
391
Kenneth Rosen Edition 7 Exercise 1.7 Question 37 (Page No. 91)
Show that the propositions $p1,p2,p3,p4,$ and $p5$ can be shown to be equivalent by proving that the conditional statements $p1 \rightarrow p4$ , $p3 \rightarrow p1$ ,$p4 \rightarrow p2$ ,$p2 \rightarrow p5$, and $p5 \rightarrow p3$ are true.
Show that the propositions $p1,p2,p3,p4,$ and $p5$ can be shown to be equivalent by proving that the conditional statements $p1 \rightarrow p4$ , $p3 \rightarrow p1$ ,$p4...
Pooja Khatri
287
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
392
Kenneth Rosen Edition 7 Exercise 1.7 Question 36 (Page No. 91)
Show that the propositions $p1,p2,p3$, and $p4$can be shown to be equivalent by showing that $p1 \leftrightarrow p4,p2 \leftrightarrow p3$, and $p1 \leftrightarrow p3$.
Show that the propositions $p1,p2,p3$, and $p4$can be shown to be equivalent by showing that $p1 \leftrightarrow p4,p2 \leftrightarrow p3$, and $p1 \leftrightarrow p3$.
Pooja Khatri
230
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
393
Kenneth Rosen Edition 7 Exercise 1.7 Question 35 (Page No. 91)
Are these steps for finding the solutions of $\sqrt{x+3=3−x}$ correct? $\sqrt{x+3=3−x}$ is given; $x+3=x2−6x+9$, obtained by squaring both sides of(1); $0=x2−7x+6$, obtained by subtracting $x+3$ from both sides of(2); $0=(x−1)(x−6)$, ... -hand side of(3); $x=1$ or $x=6$,which follows from(4) because $ab=0$ implies that $a=0$ or $b=0$.
Are these steps for finding the solutions of $\sqrt{x+3=3−x}$ correct?$\sqrt{x+3=3−x}$ is given;$x+3=x2−6x+9$, obtained by squaring both sides of(1);$0=x2−7x+6$, ...
Pooja Khatri
264
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
394
Kenneth Rosen Edition 7 Exercise 1.7 Question 34 (Page No. 91)
Is this reasoning for finding the solutions of the equation $\sqrt{2x^2−1=x}$ correct? $\sqrt{2x^2−1=x}$ is given; $2x^2−1=x^2$, obtained by squaring both sides of (1); $x^2−1=0$, obtained by subtracting $x^2$ ... left-hand side of$x^2−1$; $x=1$ or $x=−1$,which follows because $ab=0$ implies that $a=0$ or $b=0$
Is this reasoning for finding the solutions of the equation $\sqrt{2x^2−1=x}$ correct?$\sqrt{2x^2−1=x}$ is given;$2x^2−1=x^2$, obtained by squaring both sides of (1...
Pooja Khatri
268
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
1
answer
395
Kenneth Rosen Edition 7 Exercise 1.7 Question 33 (Page No. 91)
Show that these statements about the real number $x$ are equivalent: $x$ is irrational, $3x+2$ is irrational, $x/2$ is irrational.
Show that these statements about the real number $x$ are equivalent:$x$ is irrational,$3x+2$ is irrational,$x/2$ is irrational.
Pooja Khatri
600
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
396
Kenneth Rosen Edition 7 Exercise 1.7 Question 32 (Page No. 91)
Show that these statements about the real number $x$ are equivalent: $x$ is rational, $x/2$ is rational, $3x−1$ is rational.
Show that these statements about the real number $x$ are equivalent:$x$ is rational,$x/2$ is rational,$3x−1$ is rational.
Pooja Khatri
200
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
397
Kenneth Rosen Edition 7 Exercise 1.7 Question 31 (Page No. 91)
Show that these statements about the integer $x$ are equivalent: $3x+2$ is even, $x+5$ is odd, $x^2$ is even
Show that these statements about the integer $x$ are equivalent:$3x+2$ is even,$x+5$ is odd,$x^2$ is even
Pooja Khatri
257
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
398
Kenneth Rosen Edition 7 Exercise 1.7 Question 30 (Page No. 91)
Show that these three statements are equivalent, where $a$ and $b$ are real numbers: $a$ is less than $b$, the average of $a$ and $b$ is greater than $a$, and the average of $a$ and $b$ is less than $b$.
Show that these three statements are equivalent, where $a$ and $b$ are real numbers:$a$ is less than $b$,the average of $a$ and $b$ is greater than $a$, andthe average of...
Pooja Khatri
221
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
399
Kenneth Rosen Edition 7 Exercise 1.7 Question 29 (Page No. 91)
Prove or disprove that if $m$ and $n$ are integers such that $mn=1$, then either $m=1$ and $n=1$, or else $m=−1$ and $n=−1$.
Prove or disprove that if $m$ and $n$ are integers such that $mn=1$, then either $m=1$ and $n=1$, or else $m=−1$ and $n=−1$.
Pooja Khatri
202
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
400
Kenneth Rosen Edition 7 Exercise 1.7 Question 28 (Page No. 91)
Prove that $m^2 = n^2$ if and only if $m=n$ or m = -n.
Prove that $m^2 = n^2$ if and only if $m=n$ or m = -n.
Pooja Khatri
205
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
401
Kenneth Rosen Edition 7 Exercise 1.7 Question 27 (Page No. 91)
Prove that if $n$ is a positive integer, then $n$ is odd if and only if $5n+6$ is odd.
Prove that if $n$ is a positive integer, then $n$ is odd if and only if $5n+6$ is odd.
Pooja Khatri
178
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
402
Kenneth Rosen Edition 7 Exercise 1.7 Question 26 (Page No. 91)
Prove that if $n$ is a positive integer, then $n$ is even if and only if $7n+4$ is even.
Prove that if $n$ is a positive integer, then $n$ is even if and only if $7n+4$ is even.
Pooja Khatri
195
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
403
Kenneth Rosen Edition 7 Exercise 1.7 Question 25 (Page No. 91)
Use a proof by contradiction to show that there is no rational number $r$ for which $r^3+r+1=0$. [Hint:Assume that $r=a/b$ is a root, where $a$ and $b$ are integers and $a/b$ is in lowest terms. Obtain an equation involving integer $s$ by multiplying by $b^3$. Then look at whether $a$ and $b$ are each odd or even.]
Use a proof by contradiction to show that there is no rational number $r$ for which $r^3+r+1=0$. [Hint:Assume that $r=a/b$ is a root, where $a$ and $b$ are integers and $...
Pooja Khatri
235
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
404
Kenneth Rosen Edition 7 Exercise 1.7 Question 24 (Page No. 91)
Show that at least three of any $25$ days chosen must fall in the same month of the year.
Show that at least three of any $25$ days chosen must fall in the same month of the year.
Pooja Khatri
199
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
1
votes
0
answers
405
Kenneth Rosen Edition 7 Exercise 1.7 Question 23 (Page No. 91)
Show that at least ten of any $64$ days chosen must fall on the same day of the week.
Show that at least ten of any $64$ days chosen must fall on the same day of the week.
Pooja Khatri
212
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
406
Kenneth Rosen Edition 7 Exercise 1.7 Question 22 (Page No. 91)
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.
Pooja Khatri
274
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
407
Kenneth Rosen Edition 7 Exercise 1.7 Question 21 (Page No. 91)
Let $P(n)$ be the proposition “If $a$ and $b$ are positive real numbers, then $(a+b)n≥a^n+b^n.$” Prove that $P(1)$ is true. What kind of proof did you use?
Let $P(n)$ be the proposition “If $a$ and $b$ are positive real numbers, then $(a+b)n≥a^n+b^n.$” Prove that $P(1)$ is true. What kind of proof did you use?
Pooja Khatri
197
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
408
Kenneth Rosen Edition 7 Exercise 1.7 Question 20 (Page No. 91)
Prove the position $P(1)$, where $P(n)$ is the proposition “If $n$ is a positive integer greater than $1$, then $n^2 > n.$” What kind of proof did you use?
Prove the position $P(1)$, where $P(n)$ is the proposition “If $n$ is a positive integer greater than $1$, then $n^2 n.$” What kind of proof did you use?
Pooja Khatri
232
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
1
votes
0
answers
409
Kenneth Rosen Edition 7 Exercise 1.7 Question 19 (Page No. 91)
Prove the position $P(0)$, where $P(n)$ is the proposition “If $n$ is a positive integer greater than $1$, then $n^2 > n.$” What kind of proof did you use?
Prove the position $P(0)$, where $P(n)$ is the proposition “If $n$ is a positive integer greater than $1$, then $n^2 n.$” What kind of proof did you use?
Pooja Khatri
259
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
1
answer
410
Kenneth Rosen Edition 7 Exercise 1.7 Question 17 (Page No. 91)
Show that if $n$ is an integer and $n^3+5$ is odd, then $n$ is even using. a proof by contraposition. a proof by contradiction.
Show that if $n$ is an integer and $n^3+5$ is odd, then $n$ is even using.a proof by contraposition.a proof by contradiction.
Pooja Khatri
2.3k
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
1
answer
411
Kenneth Rosen Edition 7 Exercise 1.7 Question 16 (Page No. 91)
Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.
Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.
Pooja Khatri
285
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
1
answer
412
Kenneth Rosen Edition 7 Exercise 1.7 Question 15 (Page No. 91)
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.
Pooja Khatri
470
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
413
Kenneth Rosen Edition 7 Exercise 1.7 Question 14 (Page No. 91)
Prove that if $x$ is rational and $x\neq0$ , then $1/x$ is rational.
Prove that if $x$ is rational and $x\neq0$ , then $1/x$ is rational.
Pooja Khatri
175
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
414
Kenneth Rosen Edition 7 Exercise 1.7 Question 13 (Page No. 91)
Prove that if $x$ is irrational, then $1/x$ is irrational.
Prove that if $x$ is irrational, then $1/x$ is irrational.
Pooja Khatri
206
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
415
Kenneth Rosen Edition 7 Exercise 1.7 Question 12 (Page No. 91)
Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.
Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.
Pooja Khatri
329
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
1
votes
1
answer
416
Kenneth Rosen Edition 7 Exercise 1.7 Question 11 (Page No. 91)
Prove or disprove that the product of two irrational numbers is irrational.
Prove or disprove that the product of two irrational numbers is irrational.
Pooja Khatri
300
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
1
votes
1
answer
417
Kenneth Rosen Edition 7 Exercise 1.7 Question 10 (Page No. 91)
Use a direct proof to show that the product of two rational numbers is rational.
Use a direct proof to show that the product of two rational numbers is rational.
Pooja Khatri
2.6k
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
418
Kenneth Rosen Edition 7 Exercise 1.7 Question 9 (Page No. 91)
Use a proof by contradiction to prove that the sum of an irrational number and a rational number is irrational.
Use a proof by contradiction to prove that the sum of an irrational number and a rational number is irrational.
Pooja Khatri
186
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
419
Kenneth Rosen Edition 7 Exercise 1.7 Question 8 (Page No. 91)
Prove that if $n$ is a perfect square, then $n+2$ is not a perfect square
Prove that if $n$ is a perfect square, then $n+2$ is not a perfect square
Pooja Khatri
155
views
Pooja Khatri
asked
Apr 4, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
1
answer
420
Discrete Mathematics by Kenneth Rossen 7th Ed. Chapter 1 Page 89 Example 8
kaveeshnyk
660
views
kaveeshnyk
asked
Apr 1, 2019
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
+
–
Page:
« prev
1
...
9
10
11
12
13
14
15
16
17
18
19
...
35
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register