Answer to Question #181692 in Discrete Mathematics for Angelie Suarez

Question

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:

Answer 1

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.