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Activity 1, OBJECTIVE, , MATERIAL REQUIRED, , To find the number of subsets of a, given set and verify that if a set has n, number of elements, then the total, number of subsets is 2n., , Paper, different coloured pencils., , METHOD OF CONSTRUCTION, 1. Take the empty set (say) A0 which has no element., 2. Take a set (say) A1 which has one element (say) a1., 3. Take a set (say) A2 which has two elements (say) a1 and a2., 4. Take a set (say) A3 which has three elements (say) a1, a2 and a3., , DEMONSTRATION, 1. Represent A0 as in Fig. 1.1, Here the possible subsets of A0 is A0 itself, only, represented symbolically by φ. The, number of subsets of A0 is 1 = 20 ., 2. Represent A1 as in Fig. 1.2. Here the subsets, of A1 are φ, {a1}. The number of subsets of, A1 is 2 = 21, 3. Represent A2 as in Fig. 1.3, Here the subsets of A2 are φ, {a1}, {a2},, {a1, a 2}. The number of subsets of, A2 is 4 = 22., , 24/04/18

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4. Represent A3 as in Fig. 1.4, Here the subsets of A3 are φ, {a1},, {a2}, {a3),{a1, a2}, {a2, a3) ,{a3, a1), and {a 1 , a 2 , a 3}. The number of, subsets of A3 is 8 = 23., 5. Continuing this way, the number of, subsets of set A containing n, elements a1, a2, ..., an is 2n., , OBSERVATION, 1. The number of subsets of A0 is __________ = 2, 2. The number of subsets of A1 is __________ = 2, 3. The number of subsets of A2 is __________ = 2, 4. The number of subsets of A3 is __________ = 2, 5. The number of subsets of A10 is = 2, 6. The number of subsets of An is = 2, , APPLICATION, The activity can be used for calculating the number of subsets of a given set., , 12, , Laboratory Manual, , 24/04/18

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Activity 3, OBJECTIVE, , MATERIAL REQUIRED, , To represent set theoretic operations, using Venn diagrams., , Hardboard, white thick sheets of, paper, pencils, colours, scissors,, adhesive., , METHOD OF CONSTRUCTION, 1. Cut rectangular strips from a sheet of paper and paste them on a hardboard., Write the symbol U in the left/right top corner of each rectangle., 2. Draw circles A and B inside each of the rectangular strips and shade/colour, different portions as shown in Fig. 3.1 to Fig. 3.10., , DEMONSTRATION, 1. U denotes the universal set represented by the rectangle., 2. Circles A and B represent the subsets of the universal set U as shown in the, figures 3.1 to 3.10., 3. A′ denote the complement of the set A, and B′ denote the complement of, the set B as shown in the Fig. 3.3 and Fig. 3.4., 4. Coloured portion in Fig. 3.1. represents A ∪ B., , 24/04/18

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5. Coloured portion in Fig. 3.2. represents A ∩ B., , 6. Coloured portion in Fig. 3.3 represents A′, , 7. Coloured portion in Fig. 3.4 represents B′, , 8. Coloured portion in Fig. 3.5 represents (A ∩ B)′, , 17, , Mathematics, , 24/04/18

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9. Coloured portion in Fig. 3.6 represents (A ∪ B)′, , 10. Coloured portion in Fig. 3.7 represents A′ ∩ B which is same as B – A., , 11. Coloured portion in Fig. 3.8 represents A′ ∪ B., , 18, , Laboratory Manual, , 24/04/18

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12. Fig. 3.9 shows A ∩ B = φ, , 13. Fig. 3.10 shows A ⊂ B, , OBSERVATION, 1. Coloured portion in Fig. 3.1, represents ______________, 2. Coloured portion in Fig. 3.2, represents ______________, 3. Coloured portion in Fig. 3.3, represents ______________, 4. Coloured portion in Fig. 3.4, represents ______________, 5. Coloured portion in Fig. 3.5, represents ______________, 6. Coloured portion in Fig. 3.6, represents ______________, 7. Coloured portion in Fig. 3.7, represents ______________, 8. Coloured portion in Fig. 3.8, represents ______________, 9. Fig. 3.9, shows that (A ∩ B) = ______________, 10. Fig. 3.10, represents A ______________ B., , APPLICATION, Set theoretic representation of Venn diagrams are used in Logic and Mathematics., 19, , Mathematics, , 24/04/18

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Activity 4, OBJECTIVE, , MATERIAL REQUIRED, , To verify distributive law for three, given non-empty sets A, B and C, that, is, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C), , Hardboard, white thick sheets of, paper, pencil, colours, scissors,, adhesive., , METHOD OF CONSTRUCTION, 1. Cut five rectangular strips from a sheet of paper and paste them on the, hardboard in such a way that three of the rectangles are in horizontal line, and two of the remaining rectangles are also placed horizontally in a line, just below the above three rectangles. Write the symbol U in the left/right, top corner of each rectangle as shown in Fig. 4.1, Fig. 4.2, Fig. 4.3, Fig. 4.4, and Fig. 4.5., 2. Draw three circles and mark them as A, B and C in each of the five rectangles, as shown in the figures., 3. Colour/shade the portions as shown in the figures., , DEMONSTRATION, 1. U denotes the universal set represented by the rectangle in each figure., 2. Circles A, B and C represent the subsets of the universal set U., , 24/04/18

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3. In Fig. 4.1, coloured/shaded portion represents B ∩ C, coloured portions in, Fig. 4.2 represents A ∪ B, Fig. 4.3 represents A ∪ C, Fig. 4.4 represents, A ∪ ( B ∩ C) and coloured portion in Fig. 4.5 represents (A ∪ B) ∩ (A∪ C)., , OBSERVATION, 1. Coloured portion in Fig. 4.1 represents ___________., 2. Coloured portion in Fig. 4.2, represents ___________., 3. Coloured portion in Fig. 4.3, represents ___________., 4. Coloured portion in Fig. 4.4, represents ___________., 5. Coloured portion in Fig. 4.5, represents ___________., 6. The common coloured portions in Fig. 4.4 and Fig. 4.5 are __________., 7. A ∪ ( B ∩ C ) = ____________., Thus, the distributive law is verified., , APPLICATION, Distributivity property of set operations, is used in the simplification of problems, involving set operations., , NOTE, In the same way, the other distributive, law, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C), can also be verified., , 21, , Mathematics, , 24/04/18

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Activity 6, OBJECTIVE, , MATERIAL REQUIRED, , To distinguish between a Relation, and a Function., , Drawing board, coloured drawing, sheets, scissors, adhesive, strings,, nails etc., , METHOD OF CONSTRUCTION, 1. Take a drawing board/a piece of plywood of convenient size and paste a, coloured sheet on it., 2. Take a white drawing sheet and cut out a rectangular strip of size, 6 cm × 4 cm and paste it on the left side of the drawing board (see Fig. 6.1)., a, , a, , 1, b, , b, , c, , c, , Fig. 6.1, , 2, , Fig. 6.2, , a, , a, 1, , b, , 1, b, , 2, , c, , Fig. 6.3, , 2, , c, , Fig. 6.4, , 24/04/18

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a, , a, 1, , b, , 1, b, , 2, , c, , 2, , c, , Fig. 6.5, , Fig. 6.6, , 3. Fix three nails on this strip and mark them as a, b, c (see Fig. 6.1)., 4. Cut out another white rectangular strip of size 6 cm × 4 cm and paste it on, the right hand side of the drawing board., 5. Fix two nails on the right side of this strip (see Fig. 6.2) and mark them as, 1 and 2., , DEMONSTRATION, 1. Join nails of the left hand strip to the nails on the right hand strip by strings, in different ways. Some of such ways are shown in Fig. 6.3 to Fig. 6.6., 2. Joining nails in each figure constitute different ordered pairs representing, elements of a relation., , OBSERVATION, 1. In Fig. 6.3, ordered pairs are ____________., These ordered pairs constitute a ___________ but not a _________., 2. In Fig. 6.4, ordered pairs are __________. These constitute a _______ as, well as ________., 3. In Fig 6.5, ordered pairs are _______. These ordered pairs constitute a, ________ as well as ________., 4. In Fig. 6.6, ordered pairs are ________. These ordered pairs do not represent, ______ but represent ________., 25, , Mathematics, , 24/04/18

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APPLICATION, Such activity can also be used to demonstrate different types of functions such, as constant function, identity function, injective and surjective functions by, joining nails on the left hand strip to that of right hand strip in suitable manner., , NOTE, In the above activity nails have been joined in some different ways., The student may try to join them in other different ways to get more, relations of different types. The number of nails can also be changed, on both sides to represent different types of relations and functions., , 26, , Laboratory Manual, , 24/04/18