IV. Associative Laws : If A, B and C are any three sets, then (1) (A U B) U C = AU (BUC) (ii) An(BnC) = (An B)n C %3D %3D i.e., union and intersection are associative. el02 to endeplA

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A: We will prove the game statement by using the principle of mathematical induction in which we show…

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Q: Let x € Z. Prove that if 3x + 7 is even then x is odd.

A: , then we have to show  is even then  is odd

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Q: Prove the following: P(n,r)=P(n-1,r)+r.,P(n-1,r-1)

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A: that is will be...equal the 1 + 1. 1P1 + 2. 2P2 + 3. 3P3 + …. n. nPn = n+1Pn+1. and we know that nPr…

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Q: Let a; b; c 2 N such that a + b = c. Prove that gcd(a; b) = gcd(a; c) = gcd(b; c).

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