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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
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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:

  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."

This problem has been solved

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