The statement p: For any real numbers x,y if x=y, then 2x+a=2y+a when a∈Z.is trueis falseits contrapositive is not trueNone of these
Question
The statement p:
For any real numbers x, y, if x = y, then 2x + a = 2y + a when a ∈ Z.
- is true
- is false
- its contrapositive is not true
- None of these
Solution
The statement p: "For any real numbers x,y if x=y, then 2x+a=2y+a when a∈Z" is true.
Here's why:
-
The statement is saying that if x equals y, then 2x plus some integer a will equal 2y plus the same integer a.
-
If x equals y, then multiplying x and y by 2 will still result in the same number.
-
Adding the same integer a to both sides will not change the equality, because the same number is being added to both sides.
-
Therefore, the statement is true.
The contrapositive of a statement is also always true if the original statement is true. The contrapositive of this statement would be "If 2x+a does not equal 2y+a, then x does not equal y." This is also true, because if 2x+a and 2y+a are not equal, then x and y cannot be equal.
So, the correct answer is "The statement is true."
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