Question

1. In this problem, the domain of x is integers. For each of the statements, indicate whether it is TRUE or FALSE then write its negation and simplify it to the point that no ¬ symbol occurs in any of the statements (you may, however, use binary symbols such as ’̸=’ and <).

i. ∀x(x+ 2 ≠ x+3)

ii. ∃x(2x = 3x)

iii. ∃x(x^2 = x)

iv. ∀x(x^2 > 0)

v. ∃x(x^2 > 0)

2. Let A = {7,11,15}, B = {4,15,11,7,2}, C = {3,7,11,15}, D = {x ∈ Z| x is odd}. State whether each of the following statements is TRUE or FALSE and add a brief explanation why.

i. A ⊆ B

ii. B ⊆ A

iii. A⊆C

iv. A ⊂ C

v. C ⊂ A

vi. D ⊆ Z

Answer 1