q only if p. The converse of a statement is just swapping the places of the two terms.
No, the conditional statement and its converse are not negations of each other. A conditional statement has the form "If P, then Q" (P → Q), while its converse is "If Q, then P" (Q → P). The negation of a conditional statement "If P, then Q" is "P and not Q" (P ∧ ¬Q), which does not relate to the converse directly.
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
"If a number is an integer, then it is a whole number." In math terms, the converse of p-->q is q-->p. Note that although the statement in the problem is true, the converse that I just stated is not necessarily true.
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.
Only if p and q are DIFFERENT primes.
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
It is an if and only if (often shortened to iff) is usually written as p <=> q. This is also known as Equivalence. If you have a conditional p => q and it's converse q => p we can then connect them with an & we have: p => q & q => p. So, in essence, Equivalence is just a shortened version of p => q & q => p .
Converse: If p r then p q and q rContrapositive: If not p r then not (p q and q r) = If not p r then not p q or not q r Inverse: If not p q and q r then not p r = If not p q or not q r then not p r
there are 32 types of thesis statements possible
An OR with one input inverted will be either "implication" or "converse implication" depending on your point of view. Given an OR with inputs "P" and "Q", You'd invert "P" to get implication. You'd invert "Q" to get converse implication. In prose converse implication would be "P OR NOT Q".
"If a number is an integer, then it is a whole number." In math terms, the converse of p-->q is q-->p. Note that although the statement in the problem is true, the converse that I just stated is not necessarily true.
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.
The statement "p if and only if q" is true when both p and q are true, or when both p and q are false.
Construct a truth table for ~q (p q)
The statement "P and Q implies not not P or R if and only if Q" can be expressed in logical terms as ( (P \land Q) \implies (\neg \neg P \lor R) \iff Q ). This can be simplified, as (\neg \neg P) is equivalent to (P), leading to ( (P \land Q) \implies (P \lor R) \iff Q ). The implication essentially states that if both (P) and (Q) are true, then either (P) or (R) must also hold true, and this equivalence holds true only if (Q) is true. The overall expression reflects a relationship between the truth values of (P), (Q), and (R).
Only if p and q are DIFFERENT primes.
Yes.Any prime number has only 1 and itself as its factors. So given any two different primes, P and Q, the first has only 1 and P as factors while the second has only 1 and Q as factors.Since P is a prime, Q cannot be a factor of P, and since Q is a prime, P cannot be a factor of Q. Therefore P and Q are co-prime.