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)

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.

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