Question

1) Consider the real numbers<br /><br />x = 0.296×1051, y =11.2906×10−67 , z = 8.23×1035 / 2. Choose the correct statement from the following.<br /><br />(A) x, y are in scientific notation but z is not. (B) Only z is in scientific notation. B (C) None of the x, y and z is in scientific <br /><br />notation. (D) All x, y and z are in scientific notation.​

Answer 1

Step-by-step explanation:

Let the given relation defined as

R={(a,b)∣sin

2

a+cos

2

a=1}

For reflexive, sin

2

a+cos

2

a=1 (∵sin

2

θ+cos

2

θ=1,forallθ∈R)

⇒

a

R

a

⇒(a,a)∈R

⇒ R is reflexive

Foe symmetric:

sin

2

a+cos

2

b=1

⇒1−cos

2

a+1−sin

2

b=1

⇒sin

2

b+cos

2

a=1

⇒ bRa

Hence R is symmetric

For transitive:

Let aRb,bRc

⇒sin

2

a+cos

2

b=1...(i)

and sin

2

b+cos

2

c=1....(ii)

On adding eqs. (i) and (ii) we get

sin

2

a+(sin

2

b+cos

2

b)+cos

2

c=2

⇒sin

2

a+cos

2

c+1=2

⇒sin

2

a+cos

2

c=1

Hence, R is transitive also

Therefore relation R is an equivalence relation.