Use a truth table to show that the following proposition is a tautology. You must show the intermediate steps in the truth table. (Note: ⊕ means exclusive or.)
(~ (p ∨ q)) ⊕ ( (~p) → q)
Show that the following proposition is a tautology using algebraic manipulation of logical equivalences (i.e., without using a truth table). Show all your work.
( ( p ∨ q) ∧ ( p → r) ∧ ( q → r) ) → r
You should use the logical equivalences in Theorem 2.1.1 of Epp 4/e
(p. 35) or Theorem 1.1.1 of Epp 3/e (p. 14).
Show that ~ p → (q → r) and q → (p ∨ r) are logically equivalent without using truth tables.
You should use the logical equivalences in Theorem 2.1.1 of Epp 4/e
(p. 35) or Theorem 1.1.1 of Epp 3/e (p. 14).
Statements made by knights are true. Statements made by knaves are false. You meet three people: Xavier, Yolanda and Zain. You know that each is either a knight or a knave. This is what they said:
Xavier: "It is not the case that Zain is a knave."Which of Xavier, Yolanda and Zain are knights? which are knaves? Show your reasoning. Follow the format in Example 2.3.14 in Epp 4/e (p. 60) or Example 1.3.16 in Epp 3/e (p. 39).
Yolanda: "Zain and Xavier are both knights."
Zain: "Xavier is a knight or Yolanda is a knave."