symbol

[ritula]

If ° represents one of the operations +, -, and x, is k °(l + m) = (k ° 1) + (k ° m) for all numbers k, l, and m?

(A) k ° 1 is not equal to 1 ° k for some numbers k.

(B) ° represents subtraction.

Ans: D

[alescau]

(2) Simply replace ° with -.
(1) Notice that the condition is not satisfied by + and by x, therefore it must be - as in case (1).

k - l - m = 2k - l - m

now this would be true for k = 0, but the question says that it must hold for all k, thus we can say with certainty NO. Ans. D

[ritula]

But in each case, we are getting different answers like No for (1) and Yes for (2)?

(2) Simply replace ° with -.
(1) Notice that the condition is not satisfied by + and by x, therefore it must be - as in case (1).

k - l - m = 2k - l - m

now this would be true for k = 0, but the question says that it must hold for all k, thus we can say with certainty NO. Ans. D

[alescau]

yes, NO for both