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4.10.  Exercises

1.
Which of the following propositions are true?
S = { 2, x, 3, 4, 1 }
R = { a, x 2, 1 }

a) a [isin]  S	b) x [isin]  S
c) b [isin]  R	d) Ø [isin]  R
e) S [sube]  R	f) S [subset]  R
g) R [sube]  S	h) R [subset]  S

2.
Find the union, the intersection, and the set differences of A and B, where
A = { 1, 3, 4, 5, 99 } and
B = { 1, c, 99, daddy }

3.
Draw a Venn diagram for two sets A and B. Find

a) A [cap]  B	b) A [cup]  B
c) A [cap]  ~B	d) A [cup]  ~B
e) ~ (A [cap]  B )	f) ~ (A [cup]  B )

4.
Simplify: ( ~(A [cup] ~ (B [cup] C ) [cap] ~A [cap] ~( B [cap] C ) [cup] A ) )

5.
Draw a Venn diagram for two sets A and B. Find

a) ~B	b) ~ ( A [cup]  B )
c) B \ ~A	d) ~A [cup]  B
e) ~A [cap]  B	f) ~B [cap]  A
g) ( ~A [cap]  B ) [cap]  C	h) ~B [cap]  A [cap]  C
e) ( B \ ~A ) [cap]  ~C	i) ( ~A [cup]  B ) [cup]  C

6.
Draw Venn diagrams showing that:
a) ( A \ B ) \ C = ( A \ C ) \ ( B \ C )
b) A [cap]  ( ~A [cup]  B ) = A [cap]  B
c) A [cap]  ( ~A [cup]  B ) = A [cap]  B
d) B [subset]  C. Show that A [cup]  B [subset]  A [cup]  C
e) B [subset]  C. Show that A [cap]  B [subset]  A [cap]  C

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Last modified: 27/July/98 (12:14)