Write the negation of each of the following propositions without using any form of the word not:

a. Today is Thursday.

b. 2 + 1 = 3

. Without using truth tables, show that p (q r) and q (p r) are logically equivalent.

. Find the power set of each of these sets, where a is a distinct element.

a) {1, 2, 3}

b) {}

c) {, {a}}

Find union of {1, 5, 6} and {2, 5, 8}

Find intersection of {1, 3, 4, 5} and {2, 4, 5, 6} c) Let A, B and C be sets.

Show that (B A) (C A) = (B C) A 10.

Can you conclude that A = B if A , B, and C are sets such that

a) A C = B C ?

b) A C = B C ?

c) A C = B C and A C = B C ?