A conditional statement is true if, and only if, its contrapositive is true.
conditional and contrapositive + converse and inverse
The conditional statement "If A then B" is equivalent to "Not B or A" So, the inverse of "If A then B" is the inverse of "Not B or A" which is "Not not B and not A", that is "B and not A",
In order to determine if this is an inverse, you need to share the original conditional statement. With a conditional statement, you have if p, then q. The inverse of such statement is if not p then not q. Conditional statement If you like math, then you like science. Inverse If you do not like math, then you do not like science. If the conditional statement is true, the inverse is not always true (which is why it is not used in proofs). For example: Conditional Statement If two numbers are odd, then their sum is even (always true) Inverse If two numbers are not odd, then their sum is not even (never true)
No.
true
The inverse of a conditional statement switches the hypothesis and conclusion. The converse of a conditional statement switches the hypothesis and conclusion. The contrapositive of a conditional statement switches and negates the hypothesis and conclusion.
The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.
none
No, the inverse is not the negation of the converse. Actually, that is contrapositive you are referring to. The inverse is the negation of the conditional statement. For instance:P → Q~P → ~Q where ~ is the negation symbol of the sentence symbols.
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
conditional and contrapositive + converse and inverse
This would be logically equivalent to the conditional you started with.
conditional and contrapositive + converse and inverse
conditional and contrapositive + converse and inverse
conditional and contrapositive + converse and inverse
This is not always true.
Conditional statements are also called "if-then" statements.One example: "If it snows, then they cancel school."The converse of that statement is "If they cancel school, then it snows."The inverse of that statement is "If it does not snow, then they do not cancel school.The contrapositive combines the two: "If they do not cancel school, then it does not snow."In mathematics:Statement: If p, then q.Converse: If q, then p.Inverse: If not p, then not q.Contrapositive: If not q, then not p.If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.