# Propositions and Logic

**Determine the truth value of (-p and r) or -(p and q)**

**Consider the propositions below:**

**p:** 3 + 2 = 5**q:** 5 < 0**r:** 1 is a prime number

**Determine the truth value of (-p and r) or -(p and q)**

p: The truth value of ‘p’ is True or (T) for short.

q: The truth value of ‘q’ is False or (F) for short.

r: The truth value of ‘r’ is False or (F) for short.

Let’s do some boolean algebra to determine the truth value.**Note:** “-p” is equivalent to saying “not p”. Here we will use the symbol “-” to represent “not”.

(-p and r) or -(p and q)

= (-T and F) or -(T and F) ← *Substitute the propositions truth values*

= (F and F) or -(T and F) ← *(-T) A.K.A. (not T) equals F*

= (F) or -(T and F) ← *False and False is False*

= (F) or -(F) ← *True and False is False*

= (F) or (T) ← *-(F) is equal to (T)*

= (T) ← Our answer.

If you want to read up on more proposition & logic problems or Discrete Math topics in general a great book to easily learn and practice these topics is* *** Practice Problems in Discrete Mathematics by Bojana Obrenic’**, and

**.**

*Discrete Math Workbook: Interactive Exercises by James R. bush*Thanks for reading this article I hope its helpful to you all ! Keep up the learning, and if you would like more computer science, discrete math, programming and algorithm analysis videos please visit and subscribe to my YouTube channels (randerson112358 & compsci112358 )

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