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What are conditional connectives. Explain use of conditional connectives with an example?
Conditional Connectives
The statement `if p then q' is called a conditional statement and is written logically as p ! q.
(This asserts that the truth of p guarantees the truth of q.)
p ! q can also be read as `p implies q', where p is sometimes called the antecedent and qthe
consequent.
Examples:
p: It is raining.
q: I get wet.
p ! q: If it is raining, then I get wet.
s: It is Sunday.
w: I have to work today.
s ! w: If it is Sunday, then I have to work today.
»s ! w: If it is not Sunday, then I have to work today.
s !»w: If it is Sunday, I do not have to work today.
(s ^ p) !»w: If it is Sunday and it's raining, then I don't have to work today.
To examine the truth or falsity of p ! q, suppose p and q are the following propositions
p: I win the lottery,
q: I will buy you a car.
Then p ! q is the statement `If I win the lottery, then I will buy you a car'.
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