**PROPOSITIONAL LOGIC: Let p, q and r denotes the following statements: p: A square has four equal side 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 b. p ̅ → q c. q → p ̅ v r 2. Write T if the above item is true and F if it false. Show solution. (3 pts each) a. b. c. C. Show whether propositional or not p ↔ q ≡ (p → q) ^ (q → p) (8 pts) D. Find the converse, inverse and contrapositive of the implication: “If today is Monday then, I have an exam today.” (3 pts each) 1. Inverse: 2. Converse: 3. Contrapositive:**

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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)

Answer:

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

Answer: T

b. ¬p → q = ¬T → T = F → T = T

Answer: T

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

Answer: T

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

Answer: True

D. Find the converse, inverse and contrapositive of the implication: “If today is Monday then, I have an exam today.” (3 pts each)

1. Inverse: If today isn’t Monday then, I doesn’t have an exam today.

2. Converse: If I have an exam today then, today is Monday.

3. Contrapositive: If I doesn’t have an exam today then, today isn’t Monday.