RELATIONS & FUNCTIONS
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An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words or symbols). The general form of representation is (a, b) where a and b represent two distinct objects. The important thing with ordered pairs is that the ordering of the participating elements is important i.e. (a, b) is different from (b, a) unless a=b (a,b) ≠ (b,a) unless a=b Examples of Ordered pairs :(1,2)(a,b)(-172,45.98)(x,3) Remember ☞ (a, b) ≠ (b, a), unless a = b. If (a1, b2) = (a2, b2) ⇒ a1=a2 & b1=b2 Ordered pairs are widely used in set theory, calculus, relations and function theories and in the representation of intervals for functions on numbers lines and axis, for […] READ MORE...

Tuples in Relations and their examples READ MORE...

A Relation from set A to set B is defined as a set of ordered pairs formed from the elements of set A and B. In other words, a relation is a subset of the cartesian product of sets A and B. The subset is derived by establishing predicate filter(s) or criteria stating a condition that evaluates the qualifying ordered pairs from the cartesian product to be included in the subset as specified by the relation. A relation is uni-directional i.e. if a relation exists from A to B then it does not imply that a relation exists from B to A as well. Also, (a,b) ≠ (b,a) Let a ∈ A and b ∈ B. Let (a,b) be an […] READ MORE...

A function is said to be an even function if the sign of the image does not change when the sign of the preimage changes. Conversely, a function is called an odd function when the sign of the image changes when the sign of the preimage changes. For Even functions, f(x) = f(-x). For the Odd function, f(x) = -f(-x). Examples of Even Function: f(x) = x2 .We have f(1) = 1 and f(-1) = 1 hence f(1) = f(-1).This is true fora ∀ x ∈ R.Another example would be mod function |x|. Examples of Odd Function: f(x) = x3 .We have f(1) = 1 and f(-1) = -1 hence f(1) = -f(-1).This is true for ∀ x ∈ R. READ MORE...