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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.
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 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 .
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.
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.
is this statement true or falseA biconditional statement combines a conditional statement with its contrapositive.?
false
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.
What is a contra positive statement?
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.
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.
What are some examples of a conditional statement?
A simple example of a conditional statement is: If a function is differentiable, then it is continuous. An example of a converse is: Original Statement: If a number is even, then it is divisible by 2. Converse Statement: If a number is divisible by 2, then it is even. Keep in mind though, that the converse of a statement is not always true! For example: Original Statement: A triangle is a polygon. Converse Statement: A polygon is a triangle. (Clearly this last statement is not true, for example a square is a polygon, but it is certainly not a triangle!)
If a conditional statement is true then its contrapositive?
If a conditional statement is true then its contra-positive is also true.
