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Question
State, Whether the following statements are true of false.
(i) If a<b, then a−c<b−c
(ii) If a>b, then a+c>b+c
(iii) If a<b, then ac>bc
(iv) If a>b, then ac<bc
(v) If a−c>b−d; then a+d>b+c
(vi) If a<b, and c>0, then a−c>b−c where a, b, c and are real numbers and c≠0.
State, Whether the following statements are true of false.
(i) If a<b, then a−c<b−c
(ii) If a>b, then a+c>b+c
(iii) If a<b, then ac>bc
(iv) If a>b, then ac<bc
(v) If a−c>b−d; then a+d>b+c
(vi) If a<b, and c>0, then a−c>b−c where a, b, c and are real numbers and c≠0.
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Solution
(i) adding or subtracting a digit does not changes inequality sign
hence statemnet true
(ii)TRUE. same concept as above
(iii)FALSE.because multiplying with a positive number doesn't change the sign.
(iv)FALSE. Because dividing with a positive number doesn't change the sign.
(v)TRUE. AS adding or subtracting doesn't change inequality.
(vi)TRUE. same concept as above
(i) adding or subtracting a digit does not changes inequality sign
hence statemnet true
(ii)TRUE. same concept as above
(iii)FALSE.because multiplying with a positive number doesn't change the sign.
(iv)FALSE. Because dividing with a positive number doesn't change the sign.
(v)TRUE. AS adding or subtracting doesn't change inequality.
(vi)TRUE. same concept as above
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