Construct a truth table for (qvp)__> ~q
The truth table for ~q is the opposite:
q ~q
T F
F T
The truth table for conditional, p→q is true except when p is true and q is false, i.e.
p q p→q
T T T
T F F
F T T
F F T
For p∧q, the result is true only if both are true, i.e.
p q p∧q
T T T
T F F
F T F
F F F
Based on the above, you should attempt the compound truth table. Post if you have questions or need to verify your result.
Sorry, I gave the truth table for ∧ when it should be or, ∨, which is false only when both p and q are false, i.e.
p q p∨q
T T T
T F T
F T T
F F F
To construct a truth table for a logical expression, we need to consider all possible combinations of truth values for the variables involved.
In this case, we have two variables: q and p. Let's list all possible combinations of truth values for q and p:
q | p
-----------
T | T
T | F
F | T
F | F
Now, let's define the logical expression (q v p) --> ~q, where "v" represents the logical OR operator and "-->" represents the logical implication.
We can break down the expression into smaller parts:
1. q v p: This represents the logical OR of q and p.
2. ~q: This represents the negation of q.
3. (q v p) --> ~q: This represents the logical implication of (q v p) and ~q.
To evaluate the truth table, we need to apply the logical operators to the corresponding truth values. Here's how we do that:
1. q v p:
- q T v p T = T
- q T v p F = T
- q F v p T = T
- q F v p F = F
2. ~q:
- ~q T = F
- ~q F = T
3. (q v p) --> ~q:
- (q v p) T --> ~q F = F
- (q v p) T --> ~q T = T
- (q v p) F --> ~q T = T
- (q v p) F --> ~q F = T
Now, combining the results, we can construct the truth table as follows:
q | p | (q v p) --> ~q
---------------------
T | T | F
T | F | T
F | T | T
F | F | T
So, the truth table for the logical expression (q v p) --> ~q is as shown above.