Introduction to conjunction example:
The words which combine simple statements to form compound statements are called connectives. We use the connectives ‘and’, ‘or’, etc., to form new statements by combining two or more statements. But the use of these connectives in English language is not always precise and unambiguous. Hence it is necessary to define a set of connectives with definite meanings in the language of logic, called object language. Three basic connectives a conjunction which related to the English word ‘and’, ‘disjunction’ which related to the word ‘or’ ‘negation’ which corresponds to the word ‘not’.
Conjunction Example
Conjunction:
Use the symbol “?” to denote conjunction, “?” to denote disjunction and “~” to denote negation. If two simple statements p and q are connected by the word ‘and’, then the resulting compound statement ‘p and q’ is called the conjunction of p and q and is written in the symbolic form as ‘p ? q’.
Rule:
(A1) the statement p ? q has the truth value T whenever both p and q have the truth value T.
(A2) The statement p ? q has the truth value F whenever either p or q or both have the truth value F.
Ex 1: Form the conjunction of the following simple statements
P: jasmine is beautiful.
q: Joseph is intelligent.
P ? q: Jasmine beautiful and Joseph is intelligent.
Ex 2 : Form the conjunction of the following simple statements
P: Joseph goes to college.
q: Jake is intelligent.
P ? q: Joseph goes to college and Jake is intelligent.
Ex 2 : Convert the following statement into symbolic form:
‘Kim and John are going to hotel’.
The given statement can be rewritten as:
‘Kim is going to hotel’, and
‘John is going to hotel’.
Let p: Kim is going to hotel.
q: John is going to hotel.
The given statement in symbolic form is p ? q.
Conjunction Practice Problems
Form the conjunction of
Pro 1: p: Jessica reads newspaper, q : Jessica plays cricket.
Pro 2: p: I like coffee. q: I like ice-cream.
The words which combine simple statements to form compound statements are called connectives. We use the connectives ‘and’, ‘or’, etc., to form new statements by combining two or more statements. But the use of these connectives in English language is not always precise and unambiguous. Hence it is necessary to define a set of connectives with definite meanings in the language of logic, called object language. Three basic connectives a conjunction which related to the English word ‘and’, ‘disjunction’ which related to the word ‘or’ ‘negation’ which corresponds to the word ‘not’.
Conjunction Example
Conjunction:
Use the symbol “?” to denote conjunction, “?” to denote disjunction and “~” to denote negation. If two simple statements p and q are connected by the word ‘and’, then the resulting compound statement ‘p and q’ is called the conjunction of p and q and is written in the symbolic form as ‘p ? q’.
Rule:
(A1) the statement p ? q has the truth value T whenever both p and q have the truth value T.
(A2) The statement p ? q has the truth value F whenever either p or q or both have the truth value F.
Ex 1: Form the conjunction of the following simple statements
P: jasmine is beautiful.
q: Joseph is intelligent.
P ? q: Jasmine beautiful and Joseph is intelligent.
Ex 2 : Form the conjunction of the following simple statements
P: Joseph goes to college.
q: Jake is intelligent.
P ? q: Joseph goes to college and Jake is intelligent.
Ex 2 : Convert the following statement into symbolic form:
‘Kim and John are going to hotel’.
The given statement can be rewritten as:
‘Kim is going to hotel’, and
‘John is going to hotel’.
Let p: Kim is going to hotel.
q: John is going to hotel.
The given statement in symbolic form is p ? q.
Conjunction Practice Problems
Form the conjunction of
Pro 1: p: Jessica reads newspaper, q : Jessica plays cricket.
Pro 2: p: I like coffee. q: I like ice-cream.
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