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.

a) False

b) False

c) False

d) True

Step-by-step 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