Question

Check whether the following algebraic expressions are equal or not by using Tree diagrams.

(i) (x + y) + z and x + (y + z)

(ii) (p × q) × r and p × (q × r)

(iii) a – (b – c) and (a – b) – c

Answer 1

(i) (x + y) + z and x + (y + z)

The tree diagrams are

Subtraction is not associative and the expressions are not equal.

(ii) (p × q) × r and p × (q × r)

The tree diagram is

Multiplication is associative

∴ Both expressions are equal.

(iii) a – (b – c) and (a – b) – c

Their tree diagrams are

Subtraction is not associative

∴ Both expressions are not equal.