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Q: Is this statement true or falseThe conditional and contrapositive have the same truth value.?

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Conditional ConnectivesThe 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 qtheconsequent.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.Â»s ! w: If it is not Sunday, then I have to work today.s !Â»w: If it is Sunday, I do not have to work today.(s ^ p) !Â»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 propositionsp: 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'.

compound

irony

Paradox

Related questions

conditional and contrapositive + converse and inverse

conditional and contrapositive + converse and inverse

conditional and contrapositive + converse and inverse

conditional and contrapositive + converse and inverse

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The contrapostive

Truth value

It's a short statement that describes a truth, or concept.It's a short statement that describes a truth, or concept.It's a short statement that describes a truth, or concept.It's a short statement that describes a truth, or concept.It's a short statement that describes a truth, or concept.It's a short statement that describes a truth, or concept.

science

negation

Contrapositives are an idea in logic which is very useful in math.We say that A implies B if whenever Statement A is true then we know that statement B is also true.So, Say that A implies B, written:A -> BThe contrapositive of this statement is:Not-B -> Not-ARemember "A implies B" means that B must be true if A is true, so if we know that B is falce, we can deduce that A couldn't be true, so it must be falce.With truth tables it can easily be shown that"A -> B" IF AND ONLY IF "Not-B -> Not-A"So when using the contrapositive, no information is lost.In math, this is often used in proofs when, while trying to demonstrate that A implies B, it is easier to show that Not-B implies Not-A and hence that A implies B.

Conditional ConnectivesThe 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 qtheconsequent.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.Â»s ! w: If it is not Sunday, then I have to work today.s !Â»w: If it is Sunday, I do not have to work today.(s ^ p) !Â»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 propositionsp: 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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