Solution to PROPOSITIONAL LOGIC: Let p, q and r denotes the following statements: p: A square has … - Sikademy
Author Image

Archangel Macsika

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:

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

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)


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.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3168-qpid-1867