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.
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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.
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