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Computer Methods - Math Problem Example

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Summary
Above Venn diagram is made on the base of intersection between three sets, P, Q, R for example "3" is the intersection of all three sets so its is written on the place where all three circle representing the sets, intersect. Similarly "4" and "5" are intersection of sets P, Q and the sets Q,R respectively so these elements are written where this intersection point occurs…
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Computer Methods
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Download file to see previous pages S' will be computed by finding T - S, so
S' = { (1, 1), (2, 1), (2, 2) }
Question 2
1. a) Using the following propositions
h: it is humid
c: it is cloudy
and d: it is raining
express the following logical expressions in good English.
i) (hc)r
ii) (rh)c
b) Assuming and S is a set of lectures and the and the predicates
L(x): x is a lecturer
and A(x): x is articulate
write the following sentences in symbolic form
i) Larry is an articulate lecturer.
ii) There is a lecturer who is not articulate.
iii) Not every lecturer is articulate.
What is the relationship between predicates (ii) and (iii)
c) Determine the truth table for (pq)(pq)
State whether this expression is contingency, a contradiction or a tautology.
Solution
a)
i) (hc)r

the atmosphere is humid cloudy and it is not raining
ii) (rh)c

if atmosphere is raining or humid then atmosphere is cloudy.

b)
(i) Larry is an articulate lecturer.
L(Larry) A(Larry)
(ii) There is a lecturer who is not articulate.
To solve this we will use the concept of universal quantifiers $(x)
Which means that a statement is true for all values of x. Now the statement in symbolic form is:
"(x)[L(x) 'A(x)]'
Which means that "it is not true that all the lecturers are articulate". So in this sense this predicate describes that "there are some lecturers who are not articulate"

(iii) Not every lecturer is articulate.
"(x)[L(x) 'A(x)]'
The relationship between last two predicates is that these define same thing i.e. "Not every lecturer is articulate" does not ever means that " All the lecturer are not articulate" it could mean...
And all the points that are not common in any set are placed in circles where no intersection is occurring.
The relationship between last two predicates is that these define same thing i.e. "Not every lecturer is articulate" does not ever means that " All the lecturer are not articulate" it could mean that "There are some lecturers who are not articulate" so we can not use universal quantifiers for this predicate hence it means that "Not every lecture is articulate but there are some that can be articulate" so in this sense of interpretation last two predicates are same. ...Download file to see next pagesRead More
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