Question

If * and ^O are two binary operations defined by a * b = a + b and a ^O b = ab, then

• A. * is distributive on ^O.
• B. a ^O (b * c) = ac + bc
• C. (a * b) ^O c = ab + ac
• D. ^O is distributive on *.

Answer 1

The correct option is D

^O is distributive on *.

a ^O (b * c) = a ^O (b + c) = a(b + c) = ab + ac

(a ^Ob )* (a ^Oc) = ab * ac = ab + ac

Thus we note that a ^O (b * c) =(a ^Ob )* (a ^Oc)

Therefore , O distributes over *