| Class XI |
Mathematics |
Mathematics |
1 |
B. It is often convenient to usethesymbol“⇒”whichmeansimplies.Usingthissymbol,wecanwritethedefiniton of subset as follows: A ⊂ B if a ∈ A ⇒ a ∈ B W... |
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| Class XI |
Mathematics |
Mathematics |
1 |
subset of B, also B is not a subset ofA. Let A and B be two sets. If A ⊂ B and A ≠ B , then A is called a proper subset of B and B is called supers... |
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| Class XI |
Mathematics |
Mathematics |
1 |
never be a subset of itself. 1.6.1 Subsets of set of real numbers As noted in Section 1.6, there are many important subsets of R. We give below the... |
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| Class XI |
Mathematics |
Mathematics |
1 |
and is denoted by [ a, b ]. Thus [ a, b ] = {x : a ≤ x ≤ b} We can also have intervals closed at one end and open at the other, i.e., [a,b )={x : a... |
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| Class XI |
Mathematics |
Mathematics |
10 |
Let F1and F b2 the foci and O be the mid-point of the line segment F F . 1 2 O be the origin and the line through O throughF b2thepositivex-axisand... |
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| Class XI |
Mathematics |
Mathematics |
1 |
of all integers, the universal set can be the set of rational numbers or, for that matter, the set R of real numbers. For another example, in human... |
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| Class XI |
Mathematics |
Mathematics |
1 |
φ ⊂ A (xi) {φ} ⊂ A 4. Write down all the subsets of the following sets (i) {a} (ii) {a, b} (iii) {1,2,3} (iv) φ Reprint 2026-27 SETS 13 5. Writethe... |
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| Class XI |
Mathematics |
Mathematics |
1 |
sets. 1.9 Operations on Sets Inearlierclasses,wehavelearnthowtoperformtheoperationsofaddition,subtraction, multiplication and division on numbers. ... |
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| Class XI |
Mathematics |
Mathematics |
1 |
set. Solution We have, X ∪ Y = {Ram, Geeta, Akbar, David, Ashok}. This is the set of students from Class XI who are in the hockey team or the footb... |
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| Class XI |
Mathematics |
Mathematics |
11 |
coordinate system. The planes XOY, YOZ and ZOX, called, respectively the XY-plane, YZ-plane and the ZX-plane, are known as the three coordinate pla... |
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| Class XI |
Mathematics |
Mathematics |
1 |
that element ‘Geeta’is the only element common to both. Hence, X ∩ Y = {Geeta}. Example 17LetA= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, ... |
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| Class XI |
Mathematics |
Mathematics |
1 |
Figs 1.7(i)to(v) 1.9.3 Difference of sets The difference of the sets A and B in this order is the set of elements which belong toAbut not to B. Sym... |
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| Class XI |
Mathematics |
Mathematics |
1 |
{1, 2, 3} (ii) A = [ a, e, i, o, u} B = {a, b, c} (iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than ... |
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| Class XI |
Mathematics |
Mathematics |
1 |
odd natural number}andD = {x : x is a prime number }, find (i) A ∩ B (ii) A ∩ C (iii) A ∩ D (iv) B ∩ C (v) B ∩ D (vi) C ∩ D 8. Which of the followi... |
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| Class XI |
Mathematics |
Mathematics |
11 |
signs of x, y and z would change Reprint 2026-27 210 MATHEMATICS accordingly. Thus, to each point P in the space there corresponds an ordered tripl... |
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| Class XI |
Mathematics |
Mathematics |
1 |
1.10 Complement of a Set Let U be the universal set which consists of all prime numbers andAbe the subset of U which consists of all those prime nu... |
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| Class XI |
Mathematics |
Mathematics |
1 |
clearly the set of all boys in the class. Note If A is a subset of the universal set U, then its complement A′ is also a A subset of U. Again in Ex... |
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| Class XI |
Mathematics |
Mathematics |
1 |
a Venn diagram as shown in Fig 1.10. Fig 1.10 The shaded portion represents the complement of the setA. Reprint 2026-27 20 MATHEMATICS Some Propert... |
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| Class XI |
Mathematics |
Mathematics |
1 |
N and 2x + 1 > 10 } 4. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 },A= {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (i) (A ∪ B)′ = A′ ∩ B′ (ii) (A∩ B)′ =... |
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| Class XI |
Mathematics |
Mathematics |
1 |
A ⊂ B, then C – B ⊂ C – A. 6. Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B ) 7. Using properties of sets, ... |
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| Class XI |
Mathematics |
Mathematics |
1 |
all elements which are common.ThedifferenceoftwosetsAandBinthisorderisthesetofelements which belong toAbut not to B. ThecomplementofasubsetAofunive... |
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| Class XI |
Mathematics |
Mathematics |
10 |
176 MATHEMATICS Chapter 10 CONICSECTIONS v Let the relation of knowledge to real life be very visible to your pupils and let them understand how by... |
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| Class XI |
Mathematics |
Mathematics |
10 |
The intersection of the plane with the cone can take place either at the vertex of the cone or at any other part of the nappe either below or above... |
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| Class XI |
Mathematics |
Mathematics |
10 |
called the centre of the circle and the distance from the centre to a point on the circle is called the radius of the circle (Fig 10.11). Reprint 2... |
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| Class XI |
Mathematics |
Mathematics |
10 |
= 49 2 2 2 i.e. {x – (– 4)} + {y – (–5)} = 7 Therefore, the given circle has centre at (– 4, –5) and radius 7. Reprint 2026-27 CONIC SECTIONS 181 E... |
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