Question

Find the Complement of (x+6)°​

Answer 1

Answer:

Some Properties of Complement Sets

1) A ∪ A′ = U

2) A ∩ A′ = Φ

3) Law of double complement : (A′ )′ = A

4) Laws of empty set and universal set Φ′ = U and U′ = Φ.

Examples :

1) If A = { 1, 2, 3, 4} and U = { 1, 2, 3, 4, 5, 6, 7, 8} then find A complement ( A’).

Solution :

A = { 1, 2, 3, 4} and Universal set = U = { 1, 2, 3, 4, 5, 6, 7, 8}

Complement of set A contains the elements present in universal set but not in set A.

Elements are 5, 6, 7, 8.

∴ A complement = A’ = { 5, 6, 7, 8}.

2) If B = { x | x is a book on Algebra in your library} . Find B’.

Solution : B’ = { x | x is a book in your library and x ∉ B }

3) If A = { 1, 2, 3, 4, 5 } and U = N , then find A’.

Solution :

A = { 1, 2, 3, 4, 5 }

U = N

⇒ U = { 1, 2, 3, 4, 5, 6, 7, 8, 9,10,… }

A’ = { 6, 7, 8, 9, 10, … }

4) If A = { x | x is a multiple of 3, x ∉ N }. Find A’.

Solution :

As a convention, x ∉ N in the bracket indicates N is the universal set.

N = U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, … }

A = { x | x is a multiple of 3, x ∉ N }

A = { 3, 6, 9, 12, 15, … }

So, A’ = { 1, 2, 4, 5, 7, 8, 10,11

Answer 2

Answer:

We know ,

Sum of two complement angles = 90°

Let the other angle be x°

So , according to the question ,

x° + ( x + 6 )° = 90°

=> x° + x° + 6° = 90°

=> 2x° + 6° = 90°

=> 2x° = 90° - 6°

=> 2x° = 84°

=> x° = 84 / 2

=> x° = 24°

hope this much helps uh ❣️