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Set TheoryQuestion and Answers: Page 7

Question Number 1672 Answers: 2 Comments: 0

lets A and B be two finite sets, proof (or give a counter example) that ∣A∪B∣≤∣A∩B∣ ⇒ A=B

$lets A and B be two finite sets, proof (or give a counter example) that$ $∣ A \cup B ∣⩽∣ A \cap B ∣ \Rightarrow A = B$

Question Number 1616 Answers: 0 Comments: 3

lets two sets A,B and take ∣X∣ the number of elements of the set X, them proof or give a counter example that if ∣A∪B∣=∞ and ∣A∩B∣=∞ then ∣A∣=∞ and ∣B∣=∞

$lets two sets A, B and take ∣ X ∣ the number$ $of elements of the set X, them$ $proof or give a counter example that$ $if ∣ A \cup B ∣= \infty and ∣ A \cap B ∣= \infty then ∣ A ∣= \infty and ∣ B ∣= \infty$

Question Number 1132 Answers: 0 Comments: 1

let S={1,2,3,4,5}, if A,B,C is such that A∩B∩C=∅ A∩B≠∅ A∩C≠∅ how many ways can be choose A,B and C

$let S = {1, 2, 3, 4, 5}, if A, B, C is such that$ $A \cap B \cap C = \emptyset$ $A \cap B \neq \emptyset$ $A \cap C \neq \emptyset$ $how many ways can be choose A, B and$ $C$

Question Number 245 Answers: 1 Comments: 0

A={0,2,4,6,8,10} B={0,1,3,4,6,7,9} C={1,2,4,5,7,8,10} ∣(A∪B)∩(B∪C)∣

$A = {0, 2, 4, 6, 8, 10}$ $B = {0, 1, 3, 4, 6, 7, 9}$ $C = {1, 2, 4, 5, 7, 8, 10}$ $∣ (A \cup B) \cap (B \cup C) ∣$

Question Number 242 Answers: 1 Comments: 0

give the sets A={x∈N:0≤x≤9} B={0} C={1} D={2,3,5,7} E={4,6,8,9} compute ∣A\B∣+∣A\C∣+∣A\D∣+∣A\E∣ where ∣X∣=number of elements of X X\Y={x:x∈X e x∉Y} X−Y={x:x∈X e x∉Y}

$give the sets$ $A = {x \in N : 0 ⩽ x ⩽ 9}$ $B = {0}$ $C = {1}$ $D = {2, 3, 5, 7}$ $E = {4, 6, 8, 9}$ $compute$ $∣ A ∖ B ∣ + ∣ A ∖ C ∣ + ∣ A ∖ D ∣ + ∣ A ∖ E ∣$ $where$ $∣ X ∣= number of elements of X$ $X ∖ Y = {x : x \in X e x \notin Y}$ $X - Y = {x : x \in X e x \notin Y}$

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