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Let R be the relation on S = {1, 2, 3, 4, 5} defined by
R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}.
(b) Write down the matrix of R.
(c) Draw the digraph of R.
(d) Explain whether R is reáexive, irreáexive, symmetric, antisymmetric, transitive. Describe!
Intervals which extend indefinitely in both the directions are known as unbounded intervals. These are written with the aid of symbols +∞ and - ∞ . The various types
(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi
1x1
It is a fairly short section. It's real purpose is to acknowledge that the exponent properties work for any exponent. We've already used them on integer and rational exponents al
subtract 20and 10,and then mutiply by 5
Let's take a look at one more example to ensure that we've got all the ideas about limits down that we've looked at in the last couple of sections. Example: Given the below gr
provide a real-world example or scenario that can be express as a relation that is not a function
commutative law
In a two dimensional case, the form of the linear function can be obtained if we know the co-ordinates of two points on the straight line. Suppose x' and x" are two
Find out the length of the parametric curve illustrated by the following parametric equations. x = 3sin (t) y = 3 cos (t) 0 ≤ t ≤ 2? Solution We make out that thi
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