Question

give A=(1, 2) B=(x, y, z) and C=(3, 4).find AxBxC by using tree diagram.​

Answer 1

Answer:

24xyz

Step-by-step explanation:

A=(1, 2)

B=(x, y, z)

and C=(3, 4)

•A×B×C = (1×2)× (x× y× z) (3× 4)

=2×xyz×12

=24xyz

Answer 2

Answer: A × B × C = {(1, x, 3), (1, x, 4), (1, y, 3), (1, y, 4), (1, z, 3), (1, z, 4), (2, x, 3), (2, x, 4), (2, y, 3), (2, y, 4), (2, z, 3), (2, z, 4)}

Step-by-step explanation:

A × B × C

= (1, 2) × ( x, y, z) × (3, 4)

= {(1, x), (1, y), (1, z), (2, x), (2, y), (2, z)} × (3, 4)

= {(1, x, 3), (1, x, 4), (1, y, 3), (1, y, 4), (1, z, 3), (1, z, 4), (2, x, 3), (2, x, 4), (2, y, 3), (2, y, 4), (2, z, 3), (2, z, 4)}

How to check your answer if it is right?

Count the number of elements in the sets (called cardinality of the set). If the number matches with the final answer, your answer is right.

Since, A = (1, 2), B = (x, y, z), (C) = (3, 4);

then, n (A) = 2, n (B) = 3, n (C) = 2  

Thus, n (A × B × C)

= n (A) n (B) n (C)

= (2) (3) (2)

= 12

= the total number of sets in the answer

{(1, x, 3), (1, x, 4), (1, y, 3), (1, y, 4), (1, z, 3), (1, z, 4), (2, x, 3), (2, x, 4), (2, y, 3), (2, y, 4), (2, z, 3), (2, z, 4)}