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Recent questions tagged set-theory&algebra

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574
Set theory
i am not able to understand the proof. How we reached statement 2 from statement 1 as I have marked in the picture (right side) Can some one elaborate?
i am not able to understand the proof.How we reached statement 2 from statement 1 as I have marked in the picture (right side)Can some one elaborate?
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1 answer
576
Ace Test Series: Set Theory & Algebra - Relations
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________ Ans given 48 but I got 8 Please verify
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________Ans given 48but I got 8Please verify
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0 votes
1 answer
577
Kenneth Rosen Edition 6th Exercise 2.3 Question 36 (Page No. 147)
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that $f(S\cup T)=f(S)\cup f(T)$ $f(S\cap T)\subseteq f(S)\cap f(T)$ Show that inclusion in part b can be proper
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that$f(S\cup T)=f(S)\cup f(T)$$f(S\cap T)\subseteq f(S)\cap f(T)$Show that inclusion in p...
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1 votes
1 answer
578
JEST Sample Question 1-a
Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number. Then a^2 − b^ 2 is equal to (A) a − b (B) a + b (C) a × b (D) none of the above
Let a and b be positive integers such that a b and a^ 2 − b^ 2 is a prime number.Then a^2 − b^ 2 is equal to(A) a − b(B) a + b(C) a × b(D) none of the above
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3 votes
1 answer
579
JEST Sample Question 1-b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never
When is the following statement true? (A ∪ B) ∩ C = A ∩ C(A) If Ā ∩ B ∩ C = φ(B) If A ∩ B ∩ C = φ(C) always(D) never
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1 votes
1 answer
580
Jest Exam sample question-3
How many subsets of even cardinality does an n-element set have ? Justify answer. Please give a proof if possible.This is part of subjective JEST paper.
How many subsets of even cardinality does an n-element set have ? Justify answer.Please give a proof if possible.This is part of subjective JEST paper.
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1 votes
1 answer
582
MadeEasy Test Series 2019: Discrete Mathematics - Set Theory & Algebra
Which of the following are Well ordered set $\left [ Z^{+},\leq \right ]$ $\left [ Z^{-},\leq \right ]$ $\left [ Z^{+},\geq \right ]$ $\left [ Z^{-},\geq \right ]$
Which of the following are Well ordered set$\left [ Z^{+},\leq \right ]$$\left [ Z^{-},\leq \right ]$$\left [ Z^{+},\geq \right ]$$\left [ Z^{-},\geq \right ]$
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583
Testbook.com
Let f be a function from A to B and f -1 exist. Let S and T be subsets of B. Which of the following is true? 1. f -1 (S ∪ T) = f -1 (S) ∪ f -1 (T) 2. f -1 (S ∩ T) = f -1 (S) ∩ f -1 (T)
Let f be a function from A to B and f -1 exist. Let S and T be subsets of B. Which of the following is true?1. f -1 (S ∪ T) = f -1 (S) ∪ f -1 (T)2. f -1 (S ∩ T) = f...
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1 answer
584
MadeEasy Test Series: Set Thoery & Algebra - Partial Order
Let Q denote the set of rational numbers and S = {x | x belongs N ; N; x>=10} Consider the Following POSETs I. (Q ∩ [0, 1], ≤) II. (S, ≤) Which of the above POSETs are well ordered?
Let Q denote the set of rational numbers and S = {x | x belongs N ; N; x>=10}Consider the Following POSETsI. (Q ∩ [0, 1], ≤)II. (S, ≤)Which of the above POSETs are ...
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586
MADE EASY
Consider the following relations on Z∗Z. I. (a1,a2)(a1,a2) R (b1,b2)(b1,b2) iff (a1<b1(a1<b1 or (a1=b1a1=b1 ^ a2<b2a2<b2)) II (a1,a2)R(b1,b2)(a1,a2)R(b1,b2) iff (a1<b1(a1<b1 or (a1=b1a1=b1 ^ a2≤b2))a2≤b2)) Which of the above are POSETS? I I & II I, II & III
Consider the following relations on Z∗Z.I. (a1,a2)(a1,a2) R (b1,b2)(b1,b2) iff (a1<b1(a1<b1 or (a1=b1a1=b1 ^ a2<b2a2<b2))II (a1,a2)R(b1,b2)(a1,a2)R(b1,b2) iff (a1<b1(...
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0 votes
1 answer
587
Functions and Relations
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
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0 votes
1 answer
588
Functions
What Is The Total Number Of Boolean Functions Possible Over N Boolean Variables?
What Is The Total Number Of Boolean Functions Possible Over N Boolean Variables?
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0 votes
1 answer
589
Relations
Consider the following relation: $R={(x,y)| y=x^i, ∃ “i” in Z }$ R is i) Reflexive ii) Symmetric iii) Anti symmetric iv) Transitive Thanks!
Consider the following relation:$R={(x,y)| y=x^i, ∃ “i” in Z }$R isi) Reflexiveii) Symmetriciii) Anti symmetriciv) TransitiveThanks!
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2 votes
2 answers
590
group
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___
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0 votes
0 answers
591
How to solve this question
Let A be a finite non-empty set with cardinality n. Let x and y be two of the elements of A. The number of subsets S $\subseteq$ A which include at least one of x or y is
Let A be a finite non-empty set with cardinality n. Let x and y be two of the elements of A. The number of subsets S $\subseteq$ A which include at least one of x or y is...
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0 votes
0 answers
592
Madeeasy CBT1
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593
Composition of a relation- Madeeasy 2019
How to take composition of a Relation? here used concept of function but when to go with the transitivity rule concept as mentioned below? Please clarify in general when to use which method
How to take composition of a Relation? here used concept of function but when to go with the transitivity rule concept as mentioned below?Please clarify in general when t...
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0 votes
0 answers
596
Abelian Group
Prove with examples:- The set of all rational numbers except 0 are abelian group under multiplication. The set of all real numbers except 0 are closed under abelian group under multiplication.
Prove with examples:-The set of all rational numbers except 0 are abelian group under multiplication.The set of all real numbers except 0 are closed under abelian group u...
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1 votes
2 answers
599
Zeal Test Series 2019: Set Theory & Algebra - Relations
The Number of Relations, Which are both Reflexive and Symmetric but not Anti-Symmetric, on a set with 6 elements, are ____________? i got 32768 plz check
The Number of Relations, Which are both Reflexive and Symmetric but not Anti-Symmetric, on aset with 6 elements, are ____________?i got 32768 plz check
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0 votes
1 answer
600
Ace academy test series
Ans:C. Please explain
Ans:C.Please explain
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