Statements and logical operations
Answers are for parents and teachers.
1
p: “12 is divisible by 8”. Write ¬p and give the values of p and ¬p.
¬p: 12 is not divisible by 8. p is false, ¬p is true.
2
p: “2⁵ = 32”, q: “5² = 10”. Find the values of p ∧ q and p ∨ q.
p is true (32), q is false (25); p ∧ q is false, p ∨ q is true.
3
U = {1, 2, …, 24}, p: “x is a multiple of 6”, q: “x is a multiple of 4”. Find n(P ∪ Q) (4 multiples of 6, 6 multiples of 4).
8
4
Build the truth table of p ∧ ¬q for (p, q) = TT, TF, FT, FF.
F, T, F, F
5
Prove with a table: p ∨ (p ∧ q) ≡ p.
(p, q) = TT, TF, FT, FF: p ∧ q = T, F, F, F; p ∨ (p ∧ q) = T, T, F, F — the same as the column of p.