Question

Determine the truth values of these statements:

(a) The product of x2 and x3 is x6 for any real number x.
(b) x2 > 0 for any real number x.
(c) The number 315 − 8 is even.
(d) The sum of two odd integers is even.

Answer 1

a) False

b) False

c) False

d) True

Explanation:

a) False . Since x²*x³ = x²⁺³ = x⁵ , then x⁵≠x⁶ for any x≠{1,0} ( the correct statement would be x² ≥ 0 for all real numbers)

b) False . Since 0 belongs to the real numbers , then 0² = 0*0 = 0 , thus

x² is not > 0 for all real numbers ( the correct statement would be x² ≥ 0 for all real numbers)

c) False . 315 − 8 = 307 that is odd

d) True. Since odd numbers n satisfy the equation n=2*N+1 , where N is any real number , then

n₁+n₂ = 2*N₁+1 + 2*N₂+1 = 2*(N₁+N₂+1) = 2*N₃ (even) , then the sum of odds n₁+n₂ is even