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Recent questions tagged set-theory

0 votes
1 answer
96
Nptel Assignment Question
Given p, we want to prove q. Which of the following will suffice: (a) ¬q =⇒ ¬p (b) p ∧ q =⇒ q (c) ¬p ∧ ¬q =⇒ p (d) ¬q =⇒ q (e) p ∧ ¬q ∧ r =⇒ ¬r (f) none of these
Given p, we want to prove q. Which of the following will suffice:(a) ¬q =⇒ ¬p(b) p ∧ q =⇒ q(c) ¬p ∧ ¬q =⇒ p(d) ¬q =⇒ q(e) p ∧ ¬q ∧ r =⇒ ¬r(f) non...
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6 votes
1 answer
101
GATE Overflow Test Series | Mock GATE | Test 2 | Question: 1
Let $a(t), b(t),$ and $c(t)$ be the lengths of the three sides of a triangle $t$ in non-decreasing order (i.e. $a(t) \leq b(t) \leq c(t)).$ ... $X \cup Y$ $X \cap Y$ $X \oplus Y$ None of the above
Let $a(t), b(t),$ and $c(t)$ be the lengths of the three sides of a triangle $t$ in non-decreasing order (i.e. $a(t) \leq b(t) \leq c(t)).$We define the sets:$\blacksquar...
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16 votes
3 answers
102
GATE Overflow Test Series | Mock GATE | Test 2 | Question: 32
Let $S = \{1, 2, 3, 4, 5\}.$ The number of unordered pairs $A, B$ where $A$ and $B$ are disjoint subsets of $S$ is. (counting unordered pairs simply means we do not distinguish the pairs $A,B$ and $B,A)$ $243$ $125$ $122$ $257$
Let $S = \{1, 2, 3, 4, 5\}.$ The number of unordered pairs $A, B$ where $A$ and $B$ are disjoint subsets of $S$ is. (counting unordered pairs simply means we do not disti...
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2 votes
1 answer
104
NIELIT Scientist B 2020 November: 32
In a class there are 40 students who play at least one game out of Football, Cricket and Badminton. What percentage of students play only one game? $50\%$ $60\%$ $65\%$ $70\%$
In a class there are 40 students who play at least one game out of Football, Cricket and Badminton.What percentage of students play only one game?$50\%$$60\%$$65\%$$70\%$...
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2 votes
1 answer
105
NIELIT Scientist B 2020 November: 33
In a class there are 40 students who play at least one game out of Football, Cricket and Badminton. What percentage of students play all the three games? $4\%$ $5\%$ $8\%$ $10\%$
In a class there are 40 students who play at least one game out of Football, Cricket and Badminton.What percentage of students play all the three games?$4\%$$5\%$$8\%$$10...
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4 votes
1 answer
108
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 21
Let $A=\{a,b,c,d,e\}$. The total number of unordered pairs of disjoint subsets of $A$ is equal to? $3^{5}$ $5^{3}$ $102$ $122$
Let $A=\{a,b,c,d,e\}$. The total number of unordered pairs of disjoint subsets of $A$ is equal to?$3^{5}$$5^{3}$$102$$122$
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3 votes
1 answer
110
GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 4
Two finite sets $X$ and $Y$ have $m$ and $n$ elements each. The number of subsets of $X$ is $96$ more than that of $Y.$ The values of $m,n$ respectively are $4,7$ $7,4$ $5,7$ $7,5$
Two finite sets $X$ and $Y$ have $m$ and $n$ elements each. The number of subsets of $X$ is $96$ more than that of $Y.$ The values of $m,n$ respectively are$4,7$$7,4$$5,7...
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2 votes
2 answers
112
GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 9
Consider set $A = \{\phi, \{1,2\},4,\{3\}\}.$ Which of the following is a subset of $A?$ (Mark all the appropriate choices) $\{1,2\}$ $\{\{3\}\}$ $\{3\}$ $\{4,3\}$
Consider set $A = \{\phi, \{1,2\},4,\{3\}\}.$ Which of the following is a subset of $A?$ (Mark all the appropriate choices)$\{1,2\}$$\{\{3\}\}$$\{3\}$$\{4,3\}$
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2 votes
2 answers
113
GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 10
Let $A,B$ and $C$ be three sets. Then $(A-B) - C$ is _________. $(A-B)-(B-C)$ $(A-C)-(B-C)$ $(B-C)-(A-C)$ $(A-B)-(A-C)$
Let $A,B$ and $C$ be three sets. Then $(A-B) - C$ is _________.$(A-B)-(B-C)$$(A-C)-(B-C)$$(B-C)-(A-C)$$(A-B)-(A-C)$
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