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Question
Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.
Solution
We prove the statement ‘p’ is true by contrapositive method and by Direct Method.
Direct Method for any real number x, y given
x = y
⇒ 2x = 2y
⇒ 2x + a = 2y + a for some a ∈ Z.
Contrapositive Method The contrapositive statement of ‘p’ is
“For any real numbers x, y if 2x + a ≠ 2y + a
Where a ∈ Z, then x ≠ y.
Given 2x + a ≠ 2y + a
⇒ 2x ≠ 2y
⇒ x ≠ y
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