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CHAPTER
1
Critical thinking and problem solving
7
have both asthma and bronchitis? Method: draw a rectangle (
universal set
) containing
two overlapping circles A and B.
48
8
A 29
(10)
(11)
(19)
A not B
(A – Both)
B not A
(B – Both)
Both
A and B
B 30
(A not B) + Both = 29; (B not A) + Both = 30; add to give:
1) (A not B) + (B not A) + 2 × Both = 59
2) (A not B) + (B not A) + Both = 48 – 8 = 40
1) – 2) gives Both = 19
Summary
: A only = 10; B only = 11;
both A and B = 19; A + B + Both = 40; neither = 8.
Logic statements
are two premises that lead to a conclusion. For example:
• All cattle are animals.
• All bulls are cattle.
• Therefore all bulls are animals.
A
B
C
(NB: this is a logic statement diagram, not a Venn diagram)