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## Here's the Solution to this Question

PROPOSITIONAL LOGIC:

Let p, q and r denotes the following statements:

p: a square has four equal sides

q: rectangle has 2 parallel sides

r: a square is a rectangle

1. Express each of the following into English sentence. (3 pts each)

a. r ^ q → p

Answer: If a square is a rectangle and rectangle has 2 parallel sides, then a square has four equal sides

b. ¬p → q

Answer: if a square doesn’t have four equal sides, then rectangle has 2 parallel sides

c. q → ¬p v r

Answer: if rectangle has 2 parallel sides, then a square doesn’t have four equal sides or a square is a rectangle

2. Write T if the above item is true and F if it false. Show solution. (3 pts each)

p: a square has four equal sides → T

q: rectangle has 2 parallel sides → T

r: a square is a rectangle → T

a. r ^ q → p = T ^ T → T = T → T = T

b. ¬p → q = ¬T → T = F → T = T

c. q → ¬p v r = T → ¬T v T = T → F v T = F v T = T

C. Show whether propositional or not p ↔ q ≡ (p → q) ^ (q → p) (8 pts) 