p ∧ F ≡ Fp ∨ T ≡ T
To prove the statement p ∧ F ≡ Fp ∨ T ≡ T, we need to show that both sides of the equation are equivalent
To prove the statement p ∧ F ≡ Fp ∨ T ≡ T, we need to show that both sides of the equation are equivalent.
Starting with the left-hand side (LHS):
p ∧ F
The conjunction (logical AND) operator, represented by “∧”, is true only if both operands are true. In this case, p represents some proposition or statement, while F represents the logical value false.
Since one of the operands is false (F), the entire conjunction is false. Therefore, we can simplify the left-hand side as:
p ∧ F ≡ F
Now let’s evaluate the right-hand side (RHS):
Fp ∨ T
Here, Fp means the conjunction of F and p, which is false. The disjunction (logical OR) operator, represented by “∨”, is true if at least one of its operands is true.
Since one of the operands (T) is true, the whole disjunction is also true. Therefore, we can simplify the right-hand side as:
Fp ∨ T ≡ T
Comparing both sides, we have:
LHS ≡ F
RHS ≡ T
Since F and T represent different logical values, we can conclude that the original statement p ∧ F ≡ Fp ∨ T ≡ T is not true.
More Answers:
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