Construct a Truth Table for the given statement:
1. p implies ~(pVq)
2. ~(p AND q)Vp
I thought this is how to do it, but my teacher marked it incorrect:
1. p q ~(pVq) p implies ~(pVq)
T T F T implies T= T
T F F T implies F= F
F T F F implies F= T
F F T F implies T= T
2. p q ~(p AND q) ~(p AND
T T F FVT= T
T F T TVT= T
F T T TVF= T
F F T TVF= T
What did I do wrong? Did I leave out a column? Please help! Tell me everything I have to do and how to do it!
Thank you so much.
It did not put my answers in.
This was my guess for #2:
p q ~(p AND q) ~(p AND q)Vp
T T F FVT= T
T F T TVT= T
F T T TVF= T
F F T TVF= T
You'll probably need to type the answers here.
Constructing a truth table involves listing all possible combinations of truth values for the variables involved in the statement and then evaluating the expression for each combination. Let's break down the steps to create a truth table for each given statement:
1. p implies ~(pVq):
Step 1: List all possible combinations of truth values for p and q:
p q
T T
T F
F T
F F
Step 2: For each combination, evaluate ~(pVq):
p q ~(pVq)
T T F
T F T
F T F
F F T
Step 3: Evaluate p implies ~(pVq):
p q ~(pVq) p implies ~(pVq)
T T F T
T F T T
F T F T
F F T F
Your table correctly lists the values for p, q, and ~(pVq), but you made an error in the last column when evaluating p implies ~(pVq). The correct values are shown above.
2. ~(p AND q)Vp:
Step 1: List all possible combinations of truth values for p and q:
p q
T T
T F
F T
F F
Step 2: For each combination, evaluate ~(p AND q):
p q ~(p AND q)
T T F
T F T
F T T
F F T
Step 3: Evaluate ~(p AND q) V p:
p q ~(p AND q) ~(p AND q) V p
T T F T
T F T T
F T T F
F F T F
Your table correctly lists the values for p, q, and ~(p AND q), but again, there is an error in the last column when evaluating ~(p AND q) V p. The correct values are shown above.
So, to summarize, the issues were in the evaluation of the last column of each truth table. Make sure to accurately evaluate the expression for each combination of variables.