Let s be a given set and a \subset s and b \subset s. prove that a \subset b \leftrightarrow s\a \supset s\b.

Here,

S is a set so that A ⊂ S and B ⊂ S,

We have to prove that,

A ⊂ B ⇔ S\A ⊂ S\B.

Suppose,

A ⊂ B

Also, let x ∈ S\B, where, x is an arbitrary,

⇒ x ∈ S but x ∉ B

⇒ x ∈ S but x ∉ A     ( ∵ A ⊂ B )

⇒ x ∈ S\A

⇒ x ∈ S\B ⇒ x ∈ S\A

⇒ S\A ⊂ S\B.

Conversely,

Suppose, S\A ⊂ S\B,

Let y ∈ B, where y is an arbitrary,

⇒ y ∉ S - B

⇒ y ∉ S - A  ( ∵ S\A ⊂ S\B )

⇒ y ∈ A but y ∉ S

⇒ y ∈ B ⇒ y ∈ A

⇒ A ⊂ B

Hence, proved...

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

question: match the eqaution with its graph -8x - 5y = 40

answer: 8 x 5 = 40

x= absiss

y= orderly

so you have a proportional graph

question answered by

(jacemorris04)