midterm

Sets

1. The set A = { x\ x2 – 7x + 12 =0 } is
   A.{ 3 , 4 } B. { -3 , 4 } C.{ 3 , -4 } D.{ -3 , -4 } E. None of them
   2.The element(s) of A ={ (x,y)\ x+y=8 where x and y are positive integers and x≥ y} is
   1. (1,3) 2.(4,4) 3. (5,3)
      A.1 only B. 2 only C.3 only D.1 and 2 only E.2 and 3 only
      3.Given that S= {0,1,2,3,4} is the universal set and A={ x\ x3 – 9x =0 }.Then A=……..
      A.{ -3 , 0, 3 } B. { -3 , 0 } C.{ 0 , 3 } D.{ -3 , -3 } E.{0,9}
      4.The interval { x\ -2≤ x < 3 }is denoted by
      A.( -2 , 3 ) B. [ -2 , 3 ] C.[ -2 , 3 ) D.( -2 , 3 ] E. None of these
2. The graph on the number line is denoted by
   2 3
   A.(-2,3) B.[-2,3) C. (-2,3] D.[-2,3] E. Non of these
   6.If A={x\x≥4,xϵR} and B={x\x<8 ,x∈R} then A∩B is
   A. {x\8≥x≥4} B. {x\8≥x>4} C. {x\8≤x≤4}
   D. {x\8≤x<4} E.Non of these
   7.If P=[2,7) and Q=(3,7], then P∩Q =………..
   A.(3,7] B.(2,7] C.(3,7) D.[2,7] E.(4,7)
   8.Let S=R if A={x\x<a},B={x\x>a} then (A∪B)´ is
   A.∅ B.{a} C. {0} D.R{a} E.R
3. If P={x\x3+x2-6x=0 and x≥0} then P=…………
   A.{2,0,-3} B.{2} C.{2,0} D.{-2} E.{2,-3}
   10.The graph of the solution set of the inequation 5-x≥1 is
   A. B. C. D. E.
   4 4 -4 -4 -4
   11.If A={a,b,c} , B={b,c,d} and C= {a,b,e} then A∩(B∪C)=……
   A. {a,d,e} B.{a,d} C.{a,c,d} D.{a,b,d} E.{a,b,c}
4. If x∈ (P∩Q), which of the following is (are) true?
   1.x∈P 2. x∈ 3. x∈(P∪ Q)
   A.1 only B. 2only C. 1and3 only D. 2and3 only E. 1,2 and 3
5. A={x\x is an integer,1<x<12} and
   B={x\x is a positive integer and less than 15 and x is multiple of3}then A∩B is
   A.{3,6,9,12} B{2,3,4,5,6,7,8,9,10,11} C.{6,9,12} D.{3,6,9,12,15} E.{3,6,9}
   14.If A≠B, which of the following is true?
   A. A∩B=B∩A B.A∪B=B∪A C.A∪A=A D.B∩B=B
   E.A\B=B\A
   15.If S={1,2,3,4,5,6,7} is the universal set ,P={1,2,3,4} and Q´={1,2,7}, then P∩Q=…..
   A. {1,2,3} B.{3,4} C.{3} D.{4} E.∅
   16.If P∪Q={x,y,z,u,v},P∩Q={z,u} ,P\Q={x,v} then Q\P=…….
   A.{y,z,u} B. {y} C.{x,u,v} D. ∅ E. None of these
   17.Given E={2,4} ,F={4,6,8,x} The value of x such that E\F=∅
   A.0 B.2 C.4 D.6 E.8
   18.Let n(P) denotes the number of elements in set P. Given that n(P)=7 and n(Q)=3
   the largest possible value of n(P∩Q) is
   A.10 B.9 C.7 D.4 E.3

1. Let n(P) denotes the number of elements in set P. Given that n(P)=2 and n(Q)=5
   the smallest possible value of n(P∩Q) is
   A.5 B.2 C.3 D.7 E.8
   20.Which of the following is (are) true?
   1. {x\x2-5x+6=0}⊂{x\2≤x≤4}
      2.{x/x is an even number}∩{x\x is an odd number}
      3.A∪A´=S
      A.1 only B. 2 only C.3 only D . 1,2 and 3 E. None of these
      21.How many subsets of A\B if A={2,3,5,8} and B={x\x3-8x+15=0}
      A.4 B.8 C.16 D. 32 E.2
2. If A={a,b,c} and B={a,b,c,d,e} , then the number of subsets of A∩B is
   A.4 B.8 C.16 D. 32 E.2
   23.If A⊂B ,which of the following is false?
   A.A∪B=B B.A∩ E.8
   25.If n(A)=10 , n(B)=7 and n(A∩B)=4, then number of the elements of A which are not the
   element of B is
   A. 3 B.6 C. 8 D. 11 E. 14
3. If n(A∪B)=28, and n (A∩B) =9 , n(A\B)=7. then n(B\A)=……….
   A. 12 B. 16 C. 21 D. 19 E. 5
4. If A={1,3,