Question

For which of the following cases A and B are equivalent?

• A. $A=\{\frac{1}{3},\frac{1}{2},\frac{3}{5}\};B=\{x:x=\frac{n}{n+2},nϵN\}$
• B. $A=\{a,b,c,.....z\};B=\{26,25,24,....,3,2,1\}$
• C. $A=\{x:x=\frac{n^3-1}{n^3+1},nϵW,n\ge 3\};B=\{0,\frac{7}{9},\frac{13}{14}\}$
• D. $A=\{2,4,6\};B=\left\{\right(4,6),(2,6),(2,4\left)\right\}$

Answer 1

Answer: (B), (D)

$A=\{a,b,c,.....z\};B=\{26,25,24,....,3,2,1\}$
$A=\{2,4,6\};B=\left\{\right(4,6),(2,6),(2,4\left)\right\}$

Option A:

$A=\{\frac{1}{3},\frac{1}{2},\frac{3}{5}\}$

$B=\{x:x=\frac{n}{n+2},n\in N\}$

$B=\{\frac{1}{3},\frac{2}{4},\frac{3}{5}\dots \}$

$A\ne B$ , So A and B are not equivalent.

Option B:

$A=\{a,b,c\dots z\}$ and $B=\{26,25,24\dots 3,2,1\}$

Here, the numbers are in reverse order of alphabets. $\therefore$ A and B are equivalent.

Option C:

$B=\{x:x=\frac{n^3-1}{n^3+1}n\in W,n\ge 3\}$

$A=\{\frac{13}{14},\frac{63}{65},\frac{62}{63}\}$

$B=\{0,\frac{7}{9},\frac{13}{14}\}$

$A\ne B$. So A and B are not equivalent.

Option D:

$A=\{2,4,6\}$ and $B=\left\{\right(4,6),(2,6),(2,4\left)\right\}$

They are equivalent because they contain same elements.