SOLUTION: Construct a truth table for each of the following.
3) (𝑝 ∧ 𝑞) 𝑉 𝑝
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Question 1190027: Construct a truth table for each of the following.
3) (𝑝 ∧ 𝑞) 𝑉 𝑝
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
The symbol ^ means "and". It refers to a logical conjunction. In logic textbooks, the symbol ^ does not mean exponent.
The symbol v means "or". It's a logical disjunction.
Here's a truth table for p ^ qT = true, F = false
As the table shows, p ^ q is only true if BOTH p and q are true together. Otherwise, it's false.
Here's a table for p v qWe have the opposite situation going on here.
The expression p v q is only false when BOTH p and q are false together. Otherwise, it's true.
Use the ideas mentioned to get
| p | q | p ^ q | (p ^ q) v p |
| T | T | T | T |
| T | F | F | T |
| F | T | F | F |
| F | F | F | F |
That table is the final answer.
Notice how the final column is perfectly identical to the p column.
Therefore, the expression (p ^ q) v p is logically equivalent to p.
If you wanted, you can have this as scratch work off to the side somewhere
| p ^ q | p | (p ^ q) v p |
| T | T | T |
| F | T | T |
| F | F | F |
| F | F | F |
This way you can quickly compare this scratch work table to the p v q table shown earlier.
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