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By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
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.
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No, it is not valid because there is no operator between P and q.
Any fraction p/q where p is an integer and q is a non-zero integer is rational.