Short Answer TypeWrite the set of collection of all vowels of the English alphabet in roster form. Also insert the appropriate symbol of ∊ or ∉ in the blank spaces :
(i)b......A (ii) i......A (iii) O......A (iv) r......A (v)y......A (vi) a......A
List all the elements of the sets :
(a) A = { x : x is an integer,
(b) B = {x : x is a consonant of English alphabet which succeeds (comes after) letter o}
(c) C = {x : x is a natural number and x is an odd divisor of 120}
(d) D = { x : x is a letter of the word MATTERS }
(e) E = { x : x 
N, x = 3n, n 
N, n 
5}
}
N, s is a common divisor of 54 and 72}Write the following in set-builder form :
(a) A = {2, 4, 6, 8, 10......}
(b) B = {5, 10, 15, 20,...... 100}
(c) C = {1, 2, 3, 4, 6, 12, 18,36}
Match the four sets in table 1 given in set-builder form with those given in table 2 in roster form:
|
Table 1 |
Table 2 |
|
(a) {x : x is an integer and x2 + x = 0} (b) {x : x ∊ N, x < 5} (c) {x : x is a positive-integer and is a divisor of 10} (d) {x : x is positive integer and x2 < 9}. |
(i) {1,2,5,10} (ii) {1,2,3,4} (iii) {1,2} (iv) {0,-1} |
Match the sets in table 1 given in the roster form with those given in table 2 in the set-builder form :
|
Table 1 |
Table 2 |
|
(a) {A, L, G, B, R, E} (b) {2,3,7} (c) {2} (d) {-4,4} |
(i) {x : x + 5 = 7,x ∊ N} (ii) {x : x2 - 16 = 0, x ∊ R} (iii) {x : x is a prime divisor of 42} (iv) {x : x is a letter of word ALGEBRA} |
Match the equivalent sets amongst sets (i), (ii), (iii), (iv) with sets (a), (b), (c), (d).
N, x is a divisor of 6}
N, (x+1) (x-2) = 0}
}
Writing the sets in the tabular form, we have :
(i) {4, 5, 6} (ii) {a, i, o, u} (iii) {1, 2, 3, 6} (iv) {23}
(a) = {q}
(b) = {1, 2, 3}
(c) = {2, 3, 5, 7, 11}
(d) = {1, 2, 3, 4}
from above, we have number of elements in (i) is the same as those in (b), similarly, others cna be matched
Hence, (i) ~ b (ii) ~ (c) (iii) ~ (d) (iv) ~ (a)
Which of the following are examples of a null/empty set?
(a) A = {x :x ∊ N, 1 < x < 2}
(b) B = {x : x ∊ N, x < 1 or x > 3}
(c) C = {x : x ∊ N,x < 1 and x > 3}
(d) D = {x : x ∊ N, x ≤ 36}
(e) E = {x : x is an even prime number greater than 5}
State, which of the following sets are finite or infinite?
(i) {x : x ∊ Z, x2 -49 = 0} (ii) {x:x ∊ N, x < 15}
(iii) {x : x ∊ Z, x < 10} (iv) {x : x ∊ N and x is a composite number}
(v) {x : x ∊ N, x is a prime number}
(vi) {x : x is common point of two parallel straight lines l2 and l2}
(vii) The set of prime numbers less than 99.
(viii) The set of letters of English alphabet,
(ix) The set of animals living on earth. (x) {x : x is an even factor of 105}.
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