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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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Q: What are conditional connectives. Explain use of conditional connectives with an example?
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