IGNOU MTE 6 2026 - Consider the set . Define onX by.

Question

Consider the set $X = \mathbb{R} \setminus \{-1\}$ . Define * onX by

$x_1 x_2 = x_1 + x_2 + x_1x_2 \,\, \forall \,\, x_1, x_2 \in X$ .

09 Jan 2026

Answer :

Word Count : 145

Let (X=\mathbb{R}\setminus{-1}) and define (x_1*x_2=x_1+x_2+x_1x_2) for all (x_1,x_2\in X). First note that (x_1*x_2=(1+x_1)(1+x_2)-1). Since (x_1\neq -1) and (x_2\neq -1), we have (1+x_1\neq 0) and (1+x_2\neq 0), hence ((1+x_1)(1+x_2)\neq 0), so (x_1*x_2\neq -1). Thus (X) is closed under (*).

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