Associative Law of Binary Operation

Q.

Assuming the truth of P(k) and proving P(k + 1) to be true, for some integer k is known as the _______ .

1. Basic Step

2. Hypothesis step

3. Inductive Step

4. All of the these

Q. 18.solve (3/2log2 + 3/2log3 + 3/2log5)÷ (log2 + log3 - log5)

Q. Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities:
(i) $A\cup \left(B\cap C\right)=\left(A\cup B\right)\cap \left(A\cup C\right)$
(ii) $A\cap \left(B\cup C\right)=\left(A\cap B\right)\cup \left(A\cap C\right)$
(iii) $A\cap \left(B-C\right)=\left(A\cap B\right)-\left(A\cap C\right)$
(iv) $A-\left(B\cup C\right)=A\left(A-B\right)\cap \left(A-C\right)$
(v) $A-\left(B\cap C\right)=\left(A-B\right)\cup \left(A-C\right)$
(vi) $A\cap \left(B∆C\right)=\left(A\cap B\right)∆\left(A\cap C\right)$.

Q. If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:

(i) A × (B ∪ C) = (A × B) ∪ (A × C)
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
(iii) A × (B − C) = (A × B) − (A × C)

Q. For any two sets A and B if n(A) = 10, n(B) = 8 and n((A ∩ B) = 4, then value of n((A × B) ∩ (B × A)) is equal to

Q. Two sets are given as $X=\{10,11,12,13\}$ and $Y=\{2,3,4,6,12,18,36\},$ then $X\cup Y=$

1. $X$
2. $Y\cup X$
3. $\{2,3,4,6,10,11,12,13,18,36\}$
4. $Y$

Q. $\frac{n^7}{7}+\frac{n^5}{5}+\frac{n^3}{3}+\frac{n^2}{2}-\frac{37}{210}n$ is a positive integer for all n ∈ N.

Q.

We say a binary operation ${}^{\ast }$ is associative when a ${}^{\ast }$ (b ${}^{\ast }$ c) = (a ${}^{\ast }$ b) ${}^{\ast }$ (a ${}^{\ast }$c)

1. True

2. False