Determine which of the following statements are true, and which are false. Explain! (a) {a} ⊆ {a, b, c} (b) {a} ⊆ {{a, b}, c} (c) {a} ⊆ ℘({{a}, b, c})

* A propositional variable p is a formula. (It is assumed that there are infinitary many such variables p, q, r, p1, p2, ...) * If A is a formula, then (~ A) is also a formula. * If A, B are formulas, then (A A B), (A v B), (A → B), (A = B) are formulas, respectively. *if A is a formula, then •A and OA are formulas, respectively. * We use - A, AB to mean ¬A, A → B, respectively since we use the text book by Girle [1] (See below). - Exercices. Give examples of formulas and explain why they satisfy this definition.

If n(A) = 62, n(B) = 19, and n(A ∩ B) = 4, find n(A ∪ B). (A u B)

For each pair of statements, choose the one that is true. (a) (b) (c) (d) ○ {p} = {p, v} Ope {p, v} Ot ≤ {t₁ =} ○ {t} = {t₁ =} 04 ≤ (3, 4, 5) 5} 04 (3, 5, 6) O {9, 11, 13} ○ {9, 11, 13} = {1, 3, 5, 7, ...} {1, 3, 5, 7, ...) ✓