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It is often a tautology - a statement which is true bit adds nothing to anyone's knowledge. A recent example is the fatuous remark by the British Prime Minister "Brexit is Brexit".

Q: What is Vacuously true statement?

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The empty set is open because the statement: "if x in A, some neighborhood of x is a subset of A" is true! If A is empty, the hypothesis: "if x in A" is false and so the statement is vacuously true.

I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)

In computing, this is an AND statement.

No, it is not a true statement. It is a false statement.

true

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The empty set is open because the statement: "if x in A, some neighborhood of x is a subset of A" is true! If A is empty, the hypothesis: "if x in A" is false and so the statement is vacuously true.

I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)

If the statement is false, then "This statement is false", is a lie, making it "This statement is true." The statement is now true. But if the statement is true, then "This statement is false" is true, making the statement false. But if the statement is false, then "This statement is false", is a lie, making it "This statement is true." The statement is now true. But if the statement is true, then... It's one of the biggest paradoxes ever, just like saying, "I'm lying right now."

Circular logic would be a statement or series of statements that are true because of another statement, which is true because of the first. For example, statement A is true because statement B is true. Statement B is true because statement A is true

In computing, this is an AND statement.

always true

always true

Which statement is not true about characteristics of myths?Which statement is not true about characteristics of myths?

If a conditional statement is true then its contra-positive is also true.

No, it is not a true statement. It is a false statement.

true

A hypothesis is a statement.