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Sia ? 6 years, 6 months ago
f = {(1, 1), (2, 3), (0, -1), (-1, -3)}
{tex} \Rightarrow {/tex} f (1) = 1, f (2) = 3, f(0) = -1, f(-1) = -3
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Sia ? 6 years, 6 months ago
In mathematics, a function f from a set X to a set Y is surjective, or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x) = y.
Posted by George P.V 6 years, 6 months ago
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Gaurav Seth 6 years, 6 months ago
Sn=3n2+5n
S1=a1=3(1)2+5(1)=8
S2=3(2)2+5(2)=22
S2=22=a1+a2
a2=22-8=14
d=a2-a1=14-8=6
nth term value is 164,then what is n?
nth term=a+(n-1)d
164=8+(n-1)6
164-8 / 6=n-1
156/6=n-1
26+1=n
n=27
So 27thterm is 164.
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Sia ? 6 years, 6 months ago
Mathematical induction is a mathematical proof technique. It is essentially used to prove that a property P holds for every natural number n, i.e. for n = 0, 1, 2, 3, and so on.
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Gaurav Seth 6 years, 6 months ago
Let A = B
AUB = A
A intersection B = A implies A U B = A intersection B
A = B implies AU B = intersection B ---- (1)
Now let A U B = A intersection B. Then we have to prove that A = B. For this let x belongs to A implies x belongs to A U B
= x belongs to A intersection B
= x belongs to A and x Belongs to B
= x belongs to B
so A subset of B --- (2)
Now we will let y belong to B which implies y belongs to A U B
= y belongs to A intersection B
= y belongs to A and y belongs to B
= y belongs to A
Therefore, B subset of A --- (3)
from (2) and (3) we get A=B
so A union B will be equal to A intersection B implies A = B ---(4)
From (1) and (4) we will get
A union B = A INTERSECTION B Implies A = B
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The "mode" is the value that occurs most often.
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Gaurav Seth 6 years, 6 months ago
Question:
Prove that:
cot2 pi/6 + cosec 5pi/6 + 3tan2 pi/6 = 6
Solution:
L.H.S.
= R.H.S.
1Thank You