Question

(a) a (b+c) =ab + bc is known as _________________ law.

(b) Z2 X Z6 X Z3= ______________.

a) Distributive, 36
b) Commutative, 216
c) Associative, 36
d) Exponential, 36

Answer 1

The algebraic property 'a (b + c) = ab + ac' is called the distributive law, and the direct product of the groups Z2 x Z6 x Z3 has a size of 36.

Step-by-step explanation:

The expression a (b + c) = ab + ac is known as the distributive law. This law allows us to distribute the multiplication of a term over the addition of two others, which is a fundamental aspect of algebra. When it comes to the expression Z2 x Z6 x Z3, this appears to be referring to the direct product of cyclical groups in abstract algebra. The sizes of these groups are 2, 6, and 3, respectively. The size of their direct product is the product of their sizes, which is 2 x 6 x 3 = 36.