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mathematicsprinted 12 · PDF 13
165 pagesrevision 46935
printed 12 · PDF 13
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Since the pink area is common to both sets A and B, we can say that the pink
area is A ∩ B
A ∪ B is represented by the red, blue and pink areas
A′ is represented by the white and blue areas, and B′ is represented by the
white and red areas
A′ ∩ B is represented by the blue area only, and B′ ∩ A is represented by the
red area only. A′ ∩ B′ is depicted by the white area only
A′ ∪ B = A′, and B′ ∪ A = B′. A′ ∪ B′ is shown by all the area except for the pink
area
Powers and Roots
Powers
The power of a number signifies how many times a number is multiplied by
itself
For ab, a is the base and b is the power of a. a is multiplied by itself b-1 times
62 means multiplying 6 with itself once, which is 6*6 = 36
Similarly, 24 means multiplying 2 with itself thrice, which is 2*2*2*2 = 16
The power is also called the index (plural: indices) or exponent
Any number raised to the power of 1 is itself, since it is not multiplied with itself
any number of times; e.g. 51 = 5
A negative power indicates the reciprocal of the number had it been raised to
the positive power. So 3-2 is just 1/32 = 1/(3*3) = 1/9
For two terms, na and nb, na*nb = na+b. Similarly, na/nb = na-b.
n0 can be written as na-a where a can be any non-zero number. This can be
simplified to na/na = 1. Hence, n0 = 1 for any real number, n.
Roots
Roots are functions that act inversely to powers
A square root of a number is another number that when squared, equals the
original number; e.g. the square root of 25 = 5, as 52 = 25
The symbol ‘√’ depicts the square root
If another number is written before the root symbol, it means the root of that
respective power. So 3√ means the cube root. 3√27, for example, is 3; this is
because 33 = 27
Roots can be depicted as reciprocals of the original powers. So √2 is just 21/2
Note that a square root always returns a positive value, but when solving for x2
= y, both the positive and negative values of the root of y are considered. This
applies to all even powers for x