To view the information regarding different polytechnic colleges of Andhrapradesh.
Andhra Region
Osmania Region
S.V University Region
Saturday, June 6, 2009
Converse, inverse and contrapositive of a conditional
Converse, inverse and contrapositive of a conditional:
Suppose p, q are two statements.
(i) 'If q then p' is called the converse of 'If p then q'.
(ii) 'If ~p then ~q' is called the inverse of 'If p then q'.
(iii) 'If ~q then ~p' is called the contrapositive of 'If p then q'.
Symbolically,
q=>p is the converse of p=>q.
~p=>~q is the inverse of p=>q.
~q=>~p is the contrapositive of p=>q.
Suppose p, q are two statements.
(i) 'If q then p' is called the converse of 'If p then q'.
(ii) 'If ~p then ~q' is called the inverse of 'If p then q'.
(iii) 'If ~q then ~p' is called the contrapositive of 'If p then q'.
Symbolically,
q=>p is the converse of p=>q.
~p=>~q is the inverse of p=>q.
~q=>~p is the contrapositive of p=>q.
Biconditional (or Bi implication)
Biconditional (or Bi implication):
The biconditional connective <=> (read as IF AND ONLY IF) is defined by the following truth table.
Note: If p and q have the same truth value, the biconditional p <=> q is true; if p and q have opposite truth values then
p <=> q is false.
Friday, June 5, 2009
Conditional (or Implication)
Conditional (or Implication) :
The conditional connective => (read as ONLY IF) can be defined by the following truth table.
Note that the compound statement p=>q is true always except the case when p is true and q is false.
Note: A true statement can't imply a false statement.
Example: State the truth values of the following implications.
(i) If 4 * 5=20 then 4+5=9 is of truth value T.
Because p: 4*5=20, q: 4+5=9 are true statements.
Conjunction
Conjunction:
The conjunction connective ^ (read as AND) is defined by the following truth table.
AND means multiplication.
1 * 1 = 1
1 * 0 = 0
0 * 1 = 0
0 * 0 = 0
Note : The conjunction of two statements is true only when each statement is true.
Disjuction
Disjuction:
The disjunction connective v (read as OR) is defined by the following truth table.
Note: The disjunction of two statements is false only when both the statements are false.
OR means addition.
1 + 1 = 1
1 + 0= 1
0 + 1 = 0
0 +0 = 0
Negation
Negation:
Given a statement p, another statement which is the negation of p can be formed by writing the word not before p and read as not p.
The negation connective (~) is defined by the following truth table.
Example 1: p:3 is a prime number.
~p: 3 is not a prime number.
Given a statement p, another statement which is the negation of p can be formed by writing the word not before p and read as not p.
The negation connective (~) is defined by the following truth table.
Example 1: p:3 is a prime number.
~p: 3 is not a prime number.
Subscribe to:
Posts (Atom)
