RELATION
Let A and B be two nonempty sets. Then, a relation R from A to B is a subset of (A × B).
Thus, R is a relation from A to B ⇔ R ⊆ (A × B).
If (a, b) ∈ R then we say that ‘a is related to b‘ and we write, a R b.
If (a, b) ∉ R then ‘a is not related to b‘ and we write, $a \not \mathrel{R} b$.
Q1: Let A = {-1, 2, 4} and B = {1, 3}. Show A × B as arrow diagram.
A scatter plot also called scatter chart uses dots to represent data points for two different numeric variables. The position of each dot on the horizontal and vertical axis represent an individual data point.
A scatter plot is commonly used to compare distribution of two variables and to find visually any correlation between them. If there are distinct clusters/segments within the data, it will be clear in the scatter plot.
Let us try to plot a few scatter graphs using matplotlib.
A fraction is a part of whole.
Fractions are of various types. Commonly used fractions are mixed fractions, proper fractions
e.g. $ \frac{13}{4}, 2\frac{3}{4}, \frac{1}{2} $ etc.
COMPARE FRACTIONS
We can compare two or more fractions by taking the L.C.M of the denominators of the given fractions. Fraction with a greater denominator is bigger and vice versa.
Q1: Compare $\frac{23}{52} \textrm{ and } \frac{19}{22} $
Answer: $\frac{23}{52} > \frac{19}{22}$
Fill in the blanks in the following sentences with suitable word(s):
1. A collection of – 1, – 2, – 3, – 4, ... is called ________ integers.
2. Every positive integer is ________ than every negative integer.
3. Zero is ______ than every positive integer.
Q1: Simplify $\sqrt[4]{32}$ ?
Answer:
$\sqrt[4]{32} = \left ( 32 \right )^{\frac{1}{4}} $
$= \left ( 2^5 \right )^{\frac{1}{4}}$
$ = \left ( 2^4 . 2^1 \right )^{\frac{1}{4}} $
$= \left ( 2^4 \right )^{\frac{1}{4}}.(2)^{\frac{1}{4}}$
$= 2.\sqrt[4]{2}$
Q1: Define life span.
Answer: Life span is the period from birth to the natural death of an organism.
Q2: What is the life span of the following organisms?
(a) Mayfly
(b) Human Being
(c) Parrot
(d) Rice Plant
(e) Sequoia Trees
(f) Butterfly
Answer:
(a) Mayfly - 1 day
(b) Human Being - 100 years
(c) Parrot - 140 years
(d) Rice Plant - 3 to 4 months
(e) Sequoia Trees - 3000 to 4000 years
(f) Butterfly - 1 to 2 weeks
Chapter: Relations and Functions
① Let A and B be two nonempty sets. Then, the Cartesian product of A and B is the set denoted by (A×B), consisting of all ordered pairs (a, b) such that a ∈ A and b ∈ B.
∴ A × B = {(a, b): a ∈ A and b ∈ B }.
② If A = ϕ or B = ϕ (empty sets), we define A × B = ϕ
③ B × A = {(b, a) : b ∈ B and a ∈ A} and A × A = {(a,b):a,b ∈ A}.
OBJECTIVE: To draw the graph of a quadratic polynomial and observe.
(i) The shape of the curve when the coefficient of x² is positive.
(ii) The shape of the curve when the coefficient of x² is negative.
(iii) Its number of zeroes.
MATERIAL REQUIRED
Cardboard, graph paper, ruler, pencil, eraser, pen, adhesive.
Summary:
‘Fire and Ice’ is a short poem by Robert Frost. In this poem, the poet says that people knit two croaking notions about the destruction of the world. Some say it will end in fire while others say it will end in ice. According to the poet experience about human desire, he mentions that the ‘fire’ stands for desire, greed, avarice or lust. The more you try to satisfy them, the more they grow. There is no end to it. They spread rapidly like fire and engulf your whole life. One becomes selfish and sometimes cruel also. On the other hand, ‘ice’ according to the poet, stands for hatred, coldness and rigidity. One becomes insensitive and indifferent towards the feelings of others. The poet says that both fire and ice are growing with such a rapid speed that the world will soon perish either way, in fire or in ice. The poem, very artistically, underpins the philosophy that if we don’t control our emotions and let them rule us then they would bring the world to a catastrophic end.
Fill in the blanks with suitable words.
1. _________ are the substances obtained from petroleum and natural gas.
2. Petroleum is obtained from dead remains of living organisms, that is why it is called a ________ fuel.
3. Kerosene is used in ______ aircrafts.
4. In India, ________ gas has been found in Tripura, Rajasthan, Maharashtra and in the Krishna Godavari delta.
