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Earn +20 ptsQ: What is Vacuously true statement?
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Why empty set is open on the basis of def?
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.
Does a set with no element belong to any kind of set?
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.)
What is a statement that is true only if both parts of the statement are true?
In computing, this is an AND statement.
Is the equation for power is distance multiplied by time a true statement?
No, it is not a true statement. It is a false statement.
Is this statement true or falseThe (then) part of a conditional statement is the conclusion.?
true
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