Show that these compound propositions are tautologies: (1) (¬q ∧ (p → q)) → ¬p (2) ((p ∨ q) ∧ ¬p) → q
Prove that if x^3 is irrational, then x is irrational
Compute the value of the double summation: ∑4i = 1∑4j = i (3i + j)
Construct a truth table for each of these compound propositions: i) (p ⇔ q) ⇔ (r ⇔ s) ii) (p ⨁ q) ∨ (p ⨁ ¬q)
Use inference rules to deduce the following conclusions from the following sets of premises: a) Premises: p ∨ q q → r, p ∧ s → t, ¬r, ¬q → u ∧ s Conclusion: t b) Premises: (p ∧ t) → (r ∨ s), q → (u ∧ t), u → p, ¬s Co…
