Discrete Mathematics For each of the following statements do

Discrete Mathematics:

For each of the following statements do the following: (i) decide the truth value of the original statement; (ii) negate the original statement (write each negation as a complete sentence).

(a) A solution to the equation x 2 1 = 0 is x = 1.

(b) If m = 0 or n = 0 then mn = 0.

(c) For all real numbers x, x is a real number.

Decide the truth value of the statement below, then form its contrapositive (assume the context for the statement below is the set of integers): If a is divisible by 3 and b is divisible by 7, then ab is divisible by 21.

Solution

(i)

a) F

b) T

c) T

(ii)

(a) A solution to the equation x 2 1 = 0 is not x = 1.

(b) If m not equal to 0 and n not equal to 0 then mn equal to 0.

(c) For all real numbers x, x is not a real number.