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The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What we indicate by ordered pair is that the pair (a, b) is not the same pair as (b, a) unless a = b. It implies that AΧB ≠ BΧA in common. Also if A contains m kind of elements and B contains n elements then AΧB have mΧn elements.
Same as we may define AΧA = {(x, y); x€A and y€A}. We may also define cartesian product of more than two sets.
Example of Least Common Denominator: Example: Add 1/7 +2 /3 + 11/12 + 4/6 Solution: Step 1: Find out primes of each denominator. 7 = 7 (already is
ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC 2 = AP 2 + 2(1+√2)BP 2 Ans: AC = √2AB (Sinc
A subset of the real line is called as an interval. Intervals are very significant in computing inequalities or in searching domains etc. If there are two numbers a, b € R such tha
-9+f ?-1 ?? (a-1)=-12 f(-3)=2
"Prove by contradiction that no root of the equation x^18 -2x^13 + x^5 -3x^3 + x - 2 = 0 is an integer divisible by 3" Any help would be very much appreciated!
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2
The general solution of the differential equation (dy/dx) +x^2 = x^2*e^(3y). Solution)(dy/dx) +x^2 = x^2*e^(3y) dy/dx=x 2 (e 3y -1) x 2 dx=dy/(e 3y -1) this is an elementar
what is harmonic progression
Reflexive Relations: R is a reflexive relation if (a, a) € R, a € A. It could be noticed if there is at least one member a € A like (a, a) € R, then R is not reflexive. Sy
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