Hot questions in Engineering Mathematics / GATE Overflow for GATE CSE

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3561

Kenneth Rosen Edition 7 Exercise 2.2 Question 18 (Page No. 136)
Let $A,B,$ and $C$ be sets, Show that $(A \cup B) \subseteq (A \cup B \cup C),$ $(A \cap B \cap C) \subseteq (A \cap B.)$ $(A-B)-C \subseteq A-C.$ $(A-C) \cap (C-B) = \phi.$ $(B-A) \cup (C-A) = (B \cup C)- A.$

Let $A,B,$ and $C$ be sets, Show that$(A \cup B) \subseteq (A \cup B \cup C),$$(A \cap B \cap C) \subseteq (A \cap B.)$$(A-B)-C \subseteq A-C.$$(A-C) \cap (C-B) = \phi.$$...

Pooja Khatri

156 views

Pooja Khatri asked Apr 6, 2019

6 votes

1 answer

3562

MadeEasy Test Series 2018: Calculus - Limits
The value of $\lim_{x\rightarrow \infty }\left ( \frac{4^{x+2} + 3^{x}}{4^{x-2}} \right )$ is ____________

The value of $\lim_{x\rightarrow \infty }\left ( \frac{4^{x+2} + 3^{x}}{4^{x-2}} \right )$ is ____________

sumit chakraborty

712 views

sumit chakraborty asked Jan 26, 2018

0 votes

2 answers

3563

Gate 2019
What is the for the question where two statements were given as: S1: matrix A is invertible S2:|A|=0?

What is the for the question where two statements were given as:S1: matrix A is invertibleS2:|A|=0?

sai charan chakrala

974 views

sai charan chakrala asked Feb 4, 2019

0 votes

0 answers

3564

Kenneth Rosen Edition 7 Exercise 2.2 Question 19 (Page No. 136)
Show that if $A$ and $B$ are sets, then $A-B = A \cap \sim B.$ $(A \cap B) \cup (A \cap \sim B)= A.$

Show that if $A$ and $B$ are sets, then$A-B = A \cap \sim B.$$(A \cap B) \cup (A \cap \sim B)= A.$

Pooja Khatri

144 views

Pooja Khatri asked Apr 6, 2019

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0 answers

3565

Kenneth Rosen Edition 7 Exercise 2.2 Question 31 (Page No. 137)
Let $A$ and $B$ be sbusets of a universal set $U$. Show that $A \subseteq B$ if and only if $ \sim B \subseteq \sim A.$

Let $A$ and $B$ be sbusets of a universal set $U$. Show that $A \subseteq B$ if and only if $ \sim B \subseteq \sim A.$

Pooja Khatri

152 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3566

Kenneth Rosen Edition 7 Exercise 2.2 Question 8 (Page No. 136)
Prove the idempotent laws in Table 1 by showing that $A \cup A = A.$ $A \cap A=A.$

Prove the idempotent laws in Table 1 by showing that$A \cup A = A.$$A \cap A=A.$

Pooja Khatri

184 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3567

Kenneth Rosen Edition 7 Exercise 2.2 Question 7 (Page No. 136)
Prove the domination laws in Table 1 by showing that $A \cup U = U.$ $A \cap \phi=\phi.$

Prove the domination laws in Table 1 by showing that$A \cup U = U.$$A \cap \phi=\phi.$

Pooja Khatri

199 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3568

Kenneth Rosen Edition 7 Exercise 2.1 Question 40 (Page No. 126)
Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.

Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.

Pooja Khatri

199 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3569

Kenneth Rosen Edition 7 Exercise 2.2 Question 11 (Page No. 136)
Let $A$ and $B$ be sets. Prove the commutative laws from Table 1 by showing that $A \cup B = B \cup A.$ $A \cap B = B \cap A.$

Let $A$ and $B$ be sets. Prove the commutative laws from Table 1 by showing that$A \cup B = B \cup A.$$A \cap B = B \cap A.$

Pooja Khatri

137 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3570

Sheldon and Ross
Two balls each equally likely to be colored either red or blue, are put in an urn. At each stage one of the balls is randomly chosen, its color is noted, and it is then returned to the urn.if the first two balls chosen are colored red, what is the probability that a>both balls in the urn are colored red b>the next ball chosen will be red how to solve this?

Two balls each equally likely to be colored either red or blue, are put in an urn. At each stage one of the balls is randomly chosen, its color is noted, and it is then r...

DIYA BASU

1.3k views

DIYA BASU asked Feb 6, 2019

1 votes

2 answers

3571

Kenneth Rosen Edition 7 Exercise 1.3 Question 18 (Page No. 35)
show that $p \rightarrow q$ and $\sim q \rightarrow \sim p$ are logically equivalent.

show that $p \rightarrow q$ and $\sim q \rightarrow \sim p$ are logically equivalent.

Pooja Khatri

534 views

Pooja Khatri asked Mar 16, 2019

0 votes

0 answers

3572

Kenneth Rosen Edition 7 Exercise 2.1 Question 41 (Page No. 126)
Translate each of these quantifications into English and determine is truth value. $\forall x$ $\epsilon$ $(x^2 \neq -1)$ $\exists x$ $\epsilon$ $Z(x^2 =2) $ $\forall x$ $\epsilon$ $(x^2>0)$ $\forall x$ $\epsilon$ $R(x^2=x)$

Translate each of these quantifications into English and determine is truth value.$\forall x$ $\epsilon$ $(x^2 \neq -1)$$\exists x$ $\epsilon$ $Z(x^2 =2) $$\forall x$ $\e...

Pooja Khatri

240 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3573

Kenneth Rosen Edition 7 Exercise 2.1 Question 22 (Page No. 126)
Can you conclude that $A=B$ if $A$ and $B$ are two sets with the same power set?

Can you conclude that $A=B$ if $A$ and $B$ are two sets with the same power set?

Pooja Khatri

193 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3574

Kenneth Rosen Edition 7 Exercise 1.4 Question 60 (Page No. 56)
Let$P(x),Q(x),R(x)$, and $S(x)$ be the statements $x$ is a baby, $x$ is logical, $x$ is able to manage a crocodile, and $x$is despised, respectively. Suppose that the domain consists of all people. Express ... despised. Babies cannot manage crocodiles. Does (d) follow from (a), (b), and (c)? If not, is there a correct conclusion

Let$P(x),Q(x),R(x)$, and $S(x)$ be the statements “$x$ is a baby,” “$x$ is logical,” “$x$ is able to manage a crocodile,”and “$x$is despised,” respectivel...

Pooja Khatri

417 views

Pooja Khatri asked Mar 18, 2019

0 votes

0 answers

3575

Kenneth Rosen Edition 7 Exercise 2.1 Question 14 (Page No. 126)
Use a Venn diagram to illustrate the relationship $A \subseteq B$ and $B \subseteq C$.

Use a Venn diagram to illustrate the relationship $A \subseteq B$ and $B \subseteq C$.

Pooja Khatri

171 views

Pooja Khatri asked Apr 5, 2019

1 votes

1 answer

3576

Ace Test Series: Linear Algebra - Eigen Values

Sumit Kushwah

779 views

Sumit Kushwah asked Dec 7, 2018

0 votes

0 answers

3577

Kenneth Rosen Edition 7 Exercise 2.1 Question 35 (Page No. 126)
How many different elements does $A \times B$ have if $A$ has $m$ elements and $B$ has $n$ elements?

How many different elements does $A \times B$ have if $A$ has $m$ elements and $B$ has $n$ elements?

Pooja Khatri

155 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3578

Kenneth Rosen Edition 7 Exercise 2.2 Question 10 (Page No. 136)
Show that $A- \phi = A.$ $\phi-A=\phi$

Show that$A- \phi = A.$$\phi-A=\phi$

Pooja Khatri

127 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3579

Kenneth Rosen Edition 7 Exercise 2.2 Question 9 (Page No. 136)
Prove the complement laws in Table 1 by showing that $A \cup \sim A = U.$ $A \cap \sim A=\phi.$

Prove the complement laws in Table 1 by showing that$A \cup \sim A = U.$$A \cap \sim A=\phi.$

Pooja Khatri

134 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3580

Kenneth Rosen Edition 7 Exercise 1.3 Question 7 (Page No. 34)
Use De Morgan’s laws to find negation of each of the following statements. Jan is rich and happy. Carlos will bicycle or run tomorrow. Mei walks or takes the bus to class. Ibrahim is smart and hard working.

Use De Morgan’s laws to find negation of each of the following statements.Jan is rich and happy.Carlos will bicycle or run tomorrow.Mei walks or takes the bus to class....

Pooja Khatri

639 views

Pooja Khatri asked Mar 15, 2019

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