Construct a truth table for (p ^q) ->~q
What is you answer?
T T T
T F F
F T F
F F T
I think the 3rd row might be incorrect....I think maybe its F T T??
The third row is supposed to be F T T. Also, the first row should be T T F. Here's why:
If I have a dog and Joe has a cat, then Joe doesn't have a cat. Does it sound right? No; that's why it's false.
great! thank u :)
To construct a truth table for the expression "(p ^ q) -> ~q", we need to consider all possible combinations of truth values for the variables p and q.
Here's how we can do it step by step:
1. Identify the number of rows needed in the truth table based on the number of variables. Since we have two variables (p and q), we will have 2^2 = 4 rows.
2. Label the columns for p, q, (p ^ q), ~q, and the final expression.
3. Fill in the p and q columns with all possible combinations of truth (T) and falsehood (F). There will be two rows for each variable, each with a different value.
p | q |
-------
T | T |
T | F |
F | T |
F | F |
4. Evaluate the expression (p ^ q) for each row. The "^" represents the logical "AND" operator, which returns true if and only if both p and q are true.
p | q | (p ^ q) |
-----------------
T | T | T |
T | F | F |
F | T | F |
F | F | F |
5. Compute the value of ~q for each row. The "~" represents the logical "NOT" operator, which negates the truth value of q.
p | q | (p ^ q) | ~q |
----------------------
T | T | T | F |
T | F | F | T |
F | T | F | F |
F | F | F | T |
6. Finally, evaluate the entire expression "(p ^ q) -> ~q" for each row. The "->" represents the logical "IMPLICATION" operator, which returns false only if the implication's antecedent (left side) is true and the consequent (right side) is false. If so, it returns true; otherwise, it returns false.
p | q | (p ^ q) | ~q | (p ^ q) -> ~q |
---------------------------------------
T | T | T | F | F |
T | F | F | T | T |
F | T | F | F | T |
F | F | F | T | T |
This is the complete truth table for the expression "(p ^ q) -> ~q". It shows the values of the expression for all possible combinations of truth values for p and q.