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Algebra

Simple Equation Solution

Solution-1   Solution-2   Solution-3   Solution-4   Solution-5   Solution-6   Solution-7   Solution-8   Solution-9   Combined solution of problems (1 -9)     Combined solution of problems(1-9)

Solution of Simple equation

Problem: 1. 4x + 1 = 2x + 7 Solution: 4x + 1 = 2x + 7 ⇒ 4x – 2x = 7 – 1 ⇒2x = 6 ⇒ x = 3 [dividing by 2] ∴ required solution is 3. Answer: 3 Problem: 2. 5x – 3 = 2x + ...

De Morgan’s law| Algebra

If A, B are subsets of a set X then (i) X- (A∪B) = (X – A) ∩ (X– B) or, (A∪B)′ = A′∩B′. (ii) X- (A∩B) = (X – A) ∪ (X– B) or, (A∩B)′ = A′∪B′. Where we denote by A′, the complement of A. Proof: We prove ...

20 years ago, father’s was 5 times as old as his son. After 5 years three times of father’s age will be equal to five times of son’s age. What are the present age’s of father and son?

Solution: Let, the present age of the father be x and that of the son be y years. ∴ 20 years ago father was = x-20 years and 20 years ago son was = y-20 years. Again, 5 years later father will be = x+5 years ∴ 5 years later ...

Formula of cube

Formula of cube (a + b)3= a3+3a2b+3ab2+b3. (a + b)3 = a3 + b3 +3ab(a + b) Proof of formula (2): (a + b)3 = (a + b) (a + b)2 = (a + b) (a2 + 2ab + b2) = a(a2 + 2ab + b2)+ b(a2 + 2ab + ...

Formula of square

Formula of square   (a + b)2 = a2+2ab+b2   (a – b)2 = a2-2ab+b2   a2-b2 = (a + b) (a – b)   (x + a) ( x + b) = x2 + (a + b)x+ a b   (a + b +c)2 = a2 + b2 + ...

Boolean algebra

Definition: Let B be a non empty set with two binary operation + and *, a unary operation (complement), and two distinct element 0 and 1. Then B is called a Boolean algebra if the following axioms hold where a,b,c are any elements in B: [B1]   Commutative laws: (1a)      a+b=b+a                                             ...