Computer Methods - Math Problem Example

S' will be computed by finding T - S, soS' = { (1, 1), (2, 1), (2, 2) } Question 21. a) Using the following propositions h: it is humid c: it is cloudyand d: it is rainingexpress the following logical expressions in good English.i) (hc)rii) (rh)c b) Assuming and S is a set of lectures and the and the predicates L(x): x is a lecturerand A(x): x is articulatewrite the following sentences in symbolic formi) 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)rthe 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.