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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 -> B
The contrapositive of this statement is:
Not-B -> Not-A
Remember "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.
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What is contrapositive in math?
A contrapositive means that if a statement is true, than the characteristics also pertains to the other variable as well.
What is converse inverse and contrapositive?
if the statement is : if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not
What is the contrapositive of the contrapositive?
Given two propositions, p and q, start out with p implies q. For example if a number is even it is a multiple of 2. So we are saying even implies multiple of 2. Now the contrapositive is not p implies not q so if a number is not even it is not a multiple of 2. Or if not p then not q. The contrapositive of the contrapositive would negate a negation so that would make it positive. If not (not p) then not(not q) or in other words, you are back where you started, p implies q.
When you change the truth value of a given conditional statement?
by switching the truth values of the hypothesis and conclusion, it is called the contrapositive of the original statement. The contrapositive of a true conditional statement will also be true, while the contrapositive of a false conditional statement will also be false.
What is the contrapositive of the statement if it is a square then it is a rectangle?
If it is NOT a rectangle, then it is NOT a square.
