RUE or FALSE. Indicate whether each of the following is true or false. No further justification is needed.
(a) {3, c} ∈ {1, 2, 3} × {a, b, c}
(b) {} ⊆ ∅
(c) |P({10, 20, 30})| = 16.
(d) The following is a valid rule of inference: if b ∨ c and ¬c are both true, then one can conclude b is true.
(e) If p is true, q is false, and r is false, then the truth value of the statement ¬(¬p ⊕ r) → q is false.
(f) Modus tollens is the rule of inference which concludes q from the statements p and p → q.
(g) The sentence, Don’t hold your breath, is a proposition.
(h) ∀x∃y ¬P(x, y) is logically equivalent to ¬∀y∃x P(x, y).
(i) The set B = {{1, {2}}, {1}, 1, 2} has 4 elements.
(j) For all sets A and B, it is true that A ∩ B ⊆ A ∪ B.
(k) The antisymmetric property for a relation R states if (a, b) ∈ R, then (b, a) 6∈ R.
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