Select the correct option from the given alternatives:

`|("b" + "c", "c" + "a", "a" + "b"),("q" + "r", "r" + "p", "p" + "q"),(y + z, z + x, x + y)|` =

#### Options

`2|("c", "b", "a"),("r", "q", "p"),(z, y, x)|`

`2|("b", "a", "c"),("q", "p", "r"),(y, x, z)|`

`2|("a", "b", "c"),("p", "q", "r"),(x, y, z)|`

`2|("a", "c", "b"),("p", "r", "q"),(x, z, y)|`

#### Solution

**`2|("a", "b", "c"),("p", "q", "r"),(x, y, z)|`**

**Explanation;**

[Hint : `|("b" + "c", "c" + "a", "a" + "b"),("q" + "r", "r" + "p", "p" + "q"),(y+ z, z + x, x + y)|`

= `|(2("a" + "b" + "c"), "c" + "a", "a" + "b"),(2("p" + "q" + "r"), "r" + "p", "p" + "q"),(2(x + y + z), z + x, x + y)|` ...[By C_{1} + C_{2} + C_{3}]

= `2|("b", "c" + "a", "a" + "b"),("q", "r" + "p", "p" + "q"),(y, z + x, x + y)|` ...[By C_{1} – C_{2}]

= `2|("b", "c" + "a", "a"),("q", "r" + "p", "p"),(y, z + x, x)|` ...[By C_{3} – C_{1}]

= `2|("b", "c", "a"),("q", "r", "p"),(y, z, x)|` ...[By C_{2} – C_{3}]

= `-2|("b", "a", "c"),("q", "p", "r"),(y, x, z)|` ...[By C_{2} ↔ C_{3}]

= `2|("a", "b", "c"),("p", "q", "r"),(x, y, z)|` ...[By C_{1} ↔ C_{2}]