worksheet 1 on Sets

1.      State true or false

a.      The empty set has no proper subsets.

b.      If x in A’ then x not in (A’)’

c.       If n(A) = n(B) then A=B

d.      A finite set with n elements has 2ⁿ – 1 proper subsets.

e.      {x: x +2 = 3} = {x: x<2 and x in N}

2.      Write in roster form

a.      {x : x is a vowel in the word “PERPENDICULAR”}

b.      {x: x is a three digit number with zero in ten’s and one’s place}

c.       {x: x is a two digit number with the ten’s digit thrice the one’s digit}

d.      {x: x in W and 3x +2 <15}

e.      {x : 2x-1 <5 , x in I}

3.      State in the set builder form

a.      {-4,-3,-2,-1,0,1,2,3,4}

b.      {100,121,144,169,196}

c.       {88,77,66,55,44}

d.      {1, , 1/3,1/4 , 1/5 , 1/6 }

e.      {1,3,5,7,9}

4.      The set of factors of a whole number n, including n itself but not 1 is denoted by F(n).

a.      List the elements of F(16), F(40), F(16) U F(40) and F(16) intersection F(40)

b.      State the value of x for which F(16) intersection F(40) = F(x)

5.      Three sets X, Y and Z are defined as follows.

X={2,3,5}  Y={3,5,7}  Z={4,5,7,11}

a.      If P(A) means the product of the elements of set A write down the values of P(X), P(Y) and P(X intersectionY)

b.      Is it true that P(X intersectionY) is the highest factor common to P(X) and P(Y)

c.       Find out whether it is true the P(X intersection  Z) is the highest factor common to P(X) and P(Z) showing all your working.

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