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Question
If the truth value of the Boolean expression ((p ∨ q) ∧ (q→r) ∧ (∼r))→(p ∧ q) is false, then the truth values of the statements p, q, r respectively can be ______.
Options
FFT
FTF
TFT
TFF
MCQ
Fill in the Blanks
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Solution
If the truth value of the Boolean expression ((p ∨ q) ∧ (q→r) ∧ (∼r))→(p ∧ q) is false, then the truth values of the statements p, q, r respectively can be TFF.
Explanation:
| p | q | r | p ∨ q | q→r | ∼r | (p ∨ q) ∧ (q→r) ∧∼r | p ∧ q | (p ∧ q) ∧ (q→r) ∧∼r→p ∧ q |
| T | T | T | T | T | F | F | T | T |
| T | T | F | T | F | T | F | T | T |
| T | F | T | T | T | F | F | F | T |
| T | F | F | T | T | T | T | F | F |
| F | T | T | T | T | F | F | F | T |
| F | T | F | T | F | T | F | F | T |
| F | F | T | F | T | F | F | F | T |
| F | F | F | F | T | T | F | F | T |
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Logical Equivalance
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