Suppose the following two statements (x=a) ∨ (x ne a) is it true or false? I know that its false when only both operators are false, but I don't know in this case if it can be the case

Tamara Bryan 2022-07-17 Answered
Suppose the following two statements ( x = a ) ( x a ) is it true or false? I know that its false when only both operators are false, but I don't know in this case if it can be the case
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Answers (2)

Quenchingof
Answered 2022-07-18 Author has 14 answers
Step 1
For any sentence P , P ¬ P is a tautology and is therefore true.
Step 2
Consider the two possible truth values of P. Normally your sentence would have an implied quatification of x , a before it to bind the variables.
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Jadon Melendez
Answered 2022-07-19 Author has 4 answers
Step 1
You can have x = a or x a. If x = a, then x = a     x a is true since x = a is true; otherwise, if x a, then x = a     x a is true.
Step 2
In general, given a property P ¬ P is always true; similarly, P ¬ P is always false.
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