Question

Which one of the following is an elementary symmetric function of $x_1,x_2,x_3,x_4$

• A. $x_1{x}_2{x}_3+x_2{x}_3{x}_4$
• B. $x_1{x}_2+x_2{x}_3+x_1{x}_3$
• C. $x_1^2+x_2^2+x_3^2+x_4^2$
• D. $x_1{x}_2+x_1{x}_3+x_1{x}_4+x_2{x}_3+x_2{x}_4+x_3{x}_4$

Answer 1

The correct option is D $x_1{x}_2+x_1{x}_3+x_1{x}_4+x_2{x}_3+x_2{x}_4+x_3{x}_4$

$A=\{x_1,x_2,x_3,x_4\}\left(say\right)$

$\therefore$ Numbers of elements $n\left(A\right)=4$

$\therefore$ Numbers of elementary functions=${=}^4{C}_2=6$and series sets are given in (d)