No. 1. If x,y z ϵR and x + y = x + z then prove that y = z.
No. 2. If x, y ϵR and xy = 0, prove that x = 0
No. 3. For any xϵR show that | - x| = |x|
No. 4. For any x,y ϵR, prove that |x + y| ≤ | x| +|y| and hence
deduce that |x-y| ≥ | x | - | y |
No. 5. If x²> y²
prove that | x | > | y | (3 Marks)
No. 6. If | x | = | y | for any x, yϵR then give that possible
relations between x and y.
No. 7. Give the value of xϵR such that ϵR
No. 8. Give the additive inverse of -(-xy)
No. 9. If x, y ϵR and xy < 0 then
A. x > 0, y> 0 B. x >0, y <0 C. x < 0 , y < 0
No. 10. For x then x²
A. Negative B. Non-Positive C. Non-negative
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Answer:
No. 1. If x,y z ϵR and x + y = x + z then prove that y = z.
No. 2. If x, y ϵR and xy = 0, prove that x = 0
No. 3. For any xϵR show that | - x| = |x|
No. 4. For any x,y ϵR, prove that |x + y| ≤ | x| +|y| and hence
deduce that |x-y| ≥ | x | - | y |
No. 5. If x²> y²
prove that | x | > | y | (3 Marks)
No. 6. If | x | = | y | for any x, yϵR then give that possible
relations between x and y.
No. 7. Give the value of xϵR such that ϵR
No. 8. Give the additive inverse of -(-xy)
No. 9. If x, y ϵR and xy < 0 then
A. x > 0, y> 0 B. x >0, y <0 C. x < 0 , y < 0
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