Question
In: Computer Science
Create truth tables for the following expressions. Include all necessary negations and sub-expressions. ( p ∧...
Create truth tables for the following expressions. Include all necessary negations and sub-expressions.
- ( p ∧ q ) ∨ ( ¬ r )
- ¬ ( p ∨ q ) ∧ ( r ⊕ s )
- [ ( q ⊕ r ) ∧ s ] ⟶ p
If you could explain the thought process behind how you did these that would be amazing, I am trying to learn the reasoning as I practice. Thanks
Solutions
Expert Solution
Just make column for first single terms involved , then for each subexpression and then using columns of these subexpressions evaluate final expression.and also if you know the basic truth tables of or , AND , negation,xor and implication then it is pretty much simple.
( p ∧ q ) ∨ ( ¬ r )
| p | q | r | ¬ r | p ∧ q | ( p ∧ q ) ∨ ( ¬ r ) |
| T | T | T | F | T | T |
| T | T | F | T | T | T |
| T | F | T | F | F | F |
| T | F | F | T | F | T |
| F | T | T | F | F | F |
| F | T | F | T | F | T |
| F | F | T | F | F | F |
| F | F | F | T | F | T |
¬ ( p ∨ q ) ∧ ( r ⊕ s )
| p | q | r | s | p ∨ q | ¬ ( p ∨ q ) | r ⊕ s | ¬ ( p ∨ q ) ∧ ( r ⊕ s ) |
| T | T | T | T | T | F | F | F |
| T | T | T | F | T | F | T | F |
| T | T | F | T | T | F | T | F |
| T | T | F | F | T | F | F | F |
| T | F | T | T | T | F | F | F |
| T | F | T | F | T | F | T | F |
| T | F | F | T | T | F | T | F |
| T | F | F | F | T | F | F | F |
| F | T | T | T | T | F | F | F |
| F | T | T | F | T | F | T | F |
| F | T | F | T | T | F | T | F |
| F | T | F | F | T | F | F | F |
| F | F | T | T | F | T | F | F |
| F | F | T | F | F | T | T | T |
| F | F | F | T | F | T | T | T |
| F | F | F | F | F | T | F | F |
[ ( q ⊕ r ) ∧ s ] ⟶ p
| p | q | r | s | q ⊕ r | ( q ⊕ r ) ∧ s | [ ( q ⊕ r ) ∧ s ] ⟶ p |
| T | T | T | T | F | F | T |
| T | T | T | F | F | F | T |
| T | T | F | T | T | T | T |
| T | T | F | F | T | F | T |
| T | F | T | T | T | T | T |
| T | F | T | F | T | F | T |
| T | F | F | T | F | F | T |
| T | F | F | F | F | F | T |
| F | T | T | T | F | F | T |
| F | T | T | F | F | F | T |
| F | T | F | T | T | T | F |
| F | T | F | F | T | F | T |
| F | F | T | T | T | T | F |
| F | F | T | F | T | F | T |
| F | F | F | T | F | F | T |
| F | F | F | F | F | F | T |
venereology answered 2 weeks agoRelated Solutions
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