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What is a true statement that combines a true conditional statement and is its true converse?
always true
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What also is true if a conditional statement is true A its contrapositive B its converse C its inverse D none of these?
A conditional statement is true if, and only if, its contrapositive is true.
What is is called when a conditional and its converse are true and they are written as a single true statement?
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 .
Is the inverse of a conditional statement is always true?
No.
If a conditional statement is true them its contrapositive?
It may or may not be true.
is this statement true or falseThe inverse is the negation of the conditional.?
true
What is a true statement that combines a true conditional statement and its true converse?
always true
What is the conjunction of a conditional statement and its converse?
A biconditional is the conjunction of a conditional statement and its converse.
Is this statement true or falseThe conditional is the negation of the converse.?
true
What the true biconditional statement that can be formed from the conditional statement If a number is divisible by 2 then it is even and its converse.?
The true biconditional statement that can be formed is: "A number is even if and only if it is divisible by 2." This statement combines both the original conditional ("If a number is divisible by 2, then it is even") and its converse ("If a number is even, then it is divisible by 2"), establishing that the two conditions are equivalent.
Is the conditional is the negation of the Converse?
No, the conditional statement and its converse are not negations of each other. A conditional statement has the form "If P, then Q," while its converse is "If Q, then P." The negation of a conditional statement would be "P is true and Q is false," which is distinct from the converse. Thus, they represent different logical relationships.
Is this statement true or false The conditional is the negation of the converse?
The statement is false. The conditional statement "If P, then Q" and its converse "If Q, then P" are distinct statements, but the negation of the converse would be "It is not the case that if Q, then P." Thus, the conditional and the negation of the converse are not equivalent or directly related.
What also is true if a conditional statement is true A its contrapositive B its converse C its inverse D none of these?
A conditional statement is true if, and only if, its contrapositive is true.
The converse and inverse of a conditional statement are logically equivalent?
This is not always true.
Is the converse of a true conditional statement always false?
No. Consider the statement "If I'm alive, then I'm not dead." That statement is true. The converse is "If I'm not dead, then I'm alive.", which is also true.
is this statement true or falseA biconditional statement combines a conditional statement with its contrapositive.?
false
What is an example of a true conditional statement with a false converse?
A true conditional statement is "If it is raining, then the ground is wet." This statement is true because rain typically causes the ground to become wet. However, its converse, "If the ground is wet, then it is raining," is false because the ground could be wet for other reasons, such as someone watering the garden.
Is the converse of a true if-then statement never true?
Converses of a true if-then statement can be true sometimes. For example, you might have "If today is Friday, then tomorrow is Saturday," and "If tomorrow is Saturday, then today is Friday." Both the above conditional statement and its converse are true. However, sometimes a converse can be false, such as: "If an animal is a fish, then it can swim." and "If an animal can swim, it is a fish." The converse is not true, as some animals that can swim (such as otters) are not fish.
