Construct a Truth Table for the given statement:
1. p implies ~(pVq)
2. ~(p AND q)Vp
To construct a truth table for the given statements, we need to enumerate all possible combinations of truth values for the variables p and q. Since we have two variables, there will be four possible combinations.
1. p implies ~(pVq):
We start by creating a table with columns for p, q, pVq (p or q), ~(pVq) (not p or q), and p implies ~(pVq).
| p | q | pVq | ~(pVq) | p implies ~(pVq) |
|---|---|-----|--------|-----------------|
| T | T | T | F | F |
| T | F | T | F | F |
| F | T | T | F | T |
| F | F | F | T | T |
2. ~(p AND q) V p:
We create a similar table with columns for p, q, p AND q, ~(p AND q), and ~(p AND q) V p.
| p | q | p AND q | ~(p AND q) | ~(p AND q) V p |
|---|---|---------|------------|---------------|
| T | T | T | F | T |
| T | F | F | T | T |
| F | T | F | T | F |
| F | F | F | T | F |
These truth tables illustrate all possible truth values for the given logical statements.