a biconditional
"All triangles have 3 sides" and "A polygon with 3 sides is a triangle" can be combined as "A polygon is a triangle if and only if it has 3 sides."
The phrase "if and only if" is often abbreviated as "iff".
biconditional.
true
This is not always true.
This problem is a copyright violation of the curriculum used by Connections Academy, an online charter school. Students who use this problem and its answers on this website are cheating on their math test. Please remove this problem from your website.
Switching the hypothesis and conclusion of a conditional statement.
This would be logically equivalent to the conditional you started with.
yes it is
true
always true
always true
A conditional statement is true if, and only if, its contrapositive is true.
This is not always true.
A biconditional is the conjunction of a conditional statement and its converse.
A biconditional is the conjunction of a conditional statement and its converse.
the converse of this conditional is true
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.
The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.
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.