Which statement is logically equivalent to ~a �¨ b?
a �¨ ~b
b �¨ ~a
~b �¨ a
~b �¨ ~a
In Western-8859-1 encoding, the question is:
Which statement is logically equivalent to ~a → b?
a → ~b
b → ~a
~b → a
~b → ~a
~b → a is the correct answer.
Consider the statement
a=I ate
b=I am hungry
So
~a → b means
If I did not eat, I am hungry.
Try to interpret the rest of the statements, and the only one that is logically equivalent is
If I am not hungry, I ate. (~b→a)
To find the logically equivalent statement to ~a �¨ b, we can simplify the expression by using the rules of logical negation and logical conjunction.
The negation (~) of a proposition negates its truth value. In this case, ~a means "not a" and ~b means "not b".
The exclusive disjunction (�¨) is true when either one or the other proposition is true, but not both.
Let's simplify ~a �¨ b step by step:
1. Apply the rule of logical negation: ~a �¨ b becomes ~(a �¨ ~b).
This means that we negate the proposition (a �¨ ~b) by placing a negation (~) in front of it.
2. Apply the rule of De Morgan's Law: ~(p �¨ q) is logically equivalent to (~p �¦ ~q).
In our case, this means ~(a �¨ ~b) is equivalent to (~a �¦ ~~b).
3. Eliminate the double negation: ~~b is logically equivalent to b.
Therefore, (~a �¦ ~~b) becomes (~a �¦ b).
The logically equivalent statement to ~a �¨ b is (~a �¦ b).
So the correct answer is: b �¨ ~a