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 evaluate the statements for all possible combinations of truth values for the variables p and q.
1. Truth Table for p implies ~(pVq):
Create a table with columns for p, q, pVq, ~(pVq), and p implies ~(pVq).
| p | q | p V q | ~(p V q) | p implies ~(p V q) |
|-------|-------|---------|----------|-------------------|
| True | True | True | False | False |
| True | False | True | False | False |
| False | True | True | False | False |
| False | False | False | True | True |
2. Truth Table for ~(p AND q) V p:
Create a 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 |
|-------|-------|----------|------------|---------------|
| True | True | True | False | True |
| True | False | False | True | True |
| False | True | False | True | False |
| False | False | False | True | False |
These truth tables demonstrate the truth values of the given statements for all possible combinations of truth values for p and q.