Construct a truth table for each of these compound propositions: i) (p ⇔ q) ⇔ (r ⇔ s) ii) (p ⨁ q) ∨ (p ⨁ ¬q)
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i. Truth Table for: (p ⇔ q) ⇔ (r ⇔ s)
p | q | r | s | p ⇔ q | r ⇔ s | (p ⇔ q) ⇔ (r ⇔ s) |
---|---|---|---|---|---|---|
T | T | T | T | T | T | T |
T | T | T | F | T | F | F |
T | T | F | T | T | F | F |
T | T | F | F | T | T | T |
T | F | T | T | F | T | F |
T | F | T | F | F | F | T |
T | F | F | T | F | F | T |
T | F | F | F | F | T | F |
F | T | T | T | F | T | F |
F | T | T | F | F | F | T |
F | T | F | T | F | F | T |
F | T | F | F | F | T | F |
F | F | T | T | T | T | T |
F | F | T | F | T | F | F |
F | F | F | T | T | F | F |
F | F | F | F | T | T | T |
ii. Truth Table for: (p ⨁ q) ∨ (p ⨁ ¬q)
p | q | ¬q | p ⨁ q | p ⨁ ¬q | (p ⨁ q) ∨ (p ⨁ ¬q) |
---|---|---|---|---|---|
T | T | F | F | T | T |
T | F | T | T | F | T |
F | T | F | T | F | T |
F | F | T | F | T | T |