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:

1. The statement is saying that if x equals y, then 2x plus some integer a will equal 2y plus the same integer a.

2. If x equals y, then multiplying x and y by 2 will still result in the same number.

3. Adding the same integer a to both sides will not change the equality, because the same number is being added to both sides.

4. 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."

Question

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:

1. The statement is saying that if x equals y, then 2x plus some integer a will equal 2y plus the same integer a.

2. If x equals y, then multiplying x and y by 2 will still result in the same number.

3. Adding the same integer a to both sides will not change the equality, because the same number is being added to both sides.

4. 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."

Knowee AI · Accepted Answer

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:

1. The statement is saying that if x equals y, then 2x plus some integer a will equal 2y plus the same integer a.

2. If x equals y, then multiplying x and y by 2 will still result in the same number.

3. Adding the same integer a to both sides will not change the equality, because the same number is being added to both sides.

4. 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."

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

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