Ex 9.1, 6

Transcript

Ex 9.1, 6 Frame the converse for each of the propositions in Questions 1–12. Then, determine if each of the two statements is true or not. Justify the true statements and give a counterexample for each false statement. In Questions 6 and 7, x and y are real numbers. If x = y, then x² = y². Let’s write Proposition and Converse first Proposition: If 𝑥=𝑦, then 𝑥^2=𝑦^2 Converse: If 𝑥^2=𝑦^2, then 𝑥=𝑦 Checking if Proposition is true Proposition: If 𝑥=𝑦, then 𝑥^2=𝑦^2 Let’s prove this Given 𝑥=𝑦 Squaring both sides 𝑥^2=𝑦^2 Hence proved ∴ Proposition is true Checking if Converse is true Converse: If 𝑥^2=𝑦^2, then 𝑥=𝑦 Let’s prove this Let 𝑥 = 2, 𝑦 = –2 Now, 𝑥^2=2^2=4 𝑦^2=〖(−2)〗^2=4 Thus, 𝑥^2=𝑦^2 but 𝒙≠𝒚 ∴ Converse is false