Show that ¬( p ∧ q) ≡ ¬p V ¬q

Write the truth value for each of the following statements.
(1) 3 + 5 = 8 and \(\sqrt{2}\) is an irrational number.
(2) 5 is a positive integer or a square is a rectangle.
(3) Chennai is not in Tamilnadu.

In (z, *) where * is defined by a * b = a^b, prove that * is not a binary operation on z.

Let G = {1, i, -1, -i} under the binary operation multiplication. Find the inverse of all the elements.

In (z, *) where * is defined as a * b = a + b + 2. Verify the commutative and associative axiom.

Construct the truth table for (-p) v (q ∧ r)

The probability distribution of a random variable is given below

X = x	0	1	2	3	4	5	6	7
P(X = x)	0	k	2k	2k	3k	k2	2k2	7k2+k