Questions: Construct a truth table for (p ∨ q) ∨(∼ p ∨ ∼ r). Use T for true and F for false.

Construct a truth table for (p ∨ q) ∨(∼ p ∨ ∼ r). Use T for true and F for false.
Transcript text: Construct a truth table for $(p \vee q) \vee(\sim p \vee \sim r)$. Use $T$ for true and $F$ for false.
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Solution

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Solution Steps

Step 1: Identify the logical operators and statements

The logical expression involves the following statements or propositions: p, q, r. The logical expression is: (p or q) or (not p or not r). For 3 statements, there will be 8 rows in the truth table. The possible truth values combinations for the statements are: (False, False, False) (False, False, True) (False, True, False) (False, True, True) (True, False, False) (True, False, True) (True, True, False) (True, True, True) Evaluating the logical expression for each row: Given {'p': False, 'q': False, 'r': False}, the expression evaluates to True. Given {'p': False, 'q': False, 'r': True}, the expression evaluates to True. Given {'p': False, 'q': True, 'r': False}, the expression evaluates to True. Given {'p': False, 'q': True, 'r': True}, the expression evaluates to True. Given {'p': True, 'q': False, 'r': False}, the expression evaluates to True. Given {'p': True, 'q': False, 'r': True}, the expression evaluates to True. Given {'p': True, 'q': True, 'r': False}, the expression evaluates to True. Given {'p': True, 'q': True, 'r': True}, the expression evaluates to True. The complete truth table is as follows: | p | q | r | Result | |+|+|+|+| | F | F | F | T | | F | F | T | T | | F | T | F | T | | F | T | T | T | | T | F | F | T | | T | F | T | T | | T | T | F | T | | T | T | T | T |

Final Answer: The truth table has been successfully constructed based on the given logical expression.

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