conditional or implication in mathematical logic
- 5 years ago
Implication or conditional in Mathematical Logic.
Hello friends, Welcome to my channel mathstips4u.
In this channel I uploaded videos on Mathematics for the students of 11th and 12th class. In these video I have given tips and tricks that helps the students to overcome fear of facing board exam.
In my last video we have seen negation and its truth table.
In this video we are going to learn implication (or conditional) and its truth tables and some of its examples.
So we shall begin with
Implication or conditional [→]:
Let p and q be two simple statements. Then the compound statement ‘If p then q’ is called the conditional or implication, and denoted by p → q or p =＞ q. It is read as p implies q.
In the implication p → q, p is called antecedent or hypothesis and q is called the consequent or conclusion.
p → q is defined to have the truth value ‘false’ if p has truth value ‘true’ and q has truth value ‘false’. In all other cases, p → q is defined to have the truth value ‘true’.
Truth table of implication p → q
p q p → q
T T T
T F F
F T T
F F T
Remember: p → q and q → p both are not the same.
Following are phrases in English which are equivalent to (p → q)
1.p is sufficient for q.
2. q is necessary for p.
3. p only if q.
4. q follows p.
5.q provided p.
6. q if p.
Ex. Express following in symbolic form.
1. Visiting Himalayas implies peace of mind.
2. I shall come provided I finish my work.
3. A family becomes literate if the women in it are literate.
4. Rights follow from performing the duties sincerely.
5. x = 1 only if x^2 = x.
6. The sufficient condition for being rich is to be rational.
7. Getting bonus is necessary condition for me to purchase a car.
Solution:
1. Visiting Himalayas implies peace of mind.
First we write the given statement by using if …then.
‘If I visit Himalayas, then I will get peace of mind’
p: I visit Himalayas.
q: I get peace of mind.
The symbolic form is p → q.
The remaining are left intentionally as exercise for you. Try it or wait till my next video on bi-conditional is uploaded in my channel “mathstips4u”.
In this way we have seen implication and its truth tables and some of its examples.
In my next video we are going to learn Bi-conditional or double implication and its truth table.
If you like my video, please subscribe my channel, like it, share it and comment it.
Thanking you for watching my video.
Hello friends, Welcome to my channel mathstips4u.
In this channel I uploaded videos on Mathematics for the students of 11th and 12th class. In these video I have given tips and tricks that helps the students to overcome fear of facing board exam.
In my last video we have seen negation and its truth table.
In this video we are going to learn implication (or conditional) and its truth tables and some of its examples.
So we shall begin with
Implication or conditional [→]:
Let p and q be two simple statements. Then the compound statement ‘If p then q’ is called the conditional or implication, and denoted by p → q or p =＞ q. It is read as p implies q.
In the implication p → q, p is called antecedent or hypothesis and q is called the consequent or conclusion.
p → q is defined to have the truth value ‘false’ if p has truth value ‘true’ and q has truth value ‘false’. In all other cases, p → q is defined to have the truth value ‘true’.
Truth table of implication p → q
p q p → q
T T T
T F F
F T T
F F T
Remember: p → q and q → p both are not the same.
Following are phrases in English which are equivalent to (p → q)
1.p is sufficient for q.
2. q is necessary for p.
3. p only if q.
4. q follows p.
5.q provided p.
6. q if p.
Ex. Express following in symbolic form.
1. Visiting Himalayas implies peace of mind.
2. I shall come provided I finish my work.
3. A family becomes literate if the women in it are literate.
4. Rights follow from performing the duties sincerely.
5. x = 1 only if x^2 = x.
6. The sufficient condition for being rich is to be rational.
7. Getting bonus is necessary condition for me to purchase a car.
Solution:
1. Visiting Himalayas implies peace of mind.
First we write the given statement by using if …then.
‘If I visit Himalayas, then I will get peace of mind’
p: I visit Himalayas.
q: I get peace of mind.
The symbolic form is p → q.
The remaining are left intentionally as exercise for you. Try it or wait till my next video on bi-conditional is uploaded in my channel “mathstips4u”.
In this way we have seen implication and its truth tables and some of its examples.
In my next video we are going to learn Bi-conditional or double implication and its truth table.
If you like my video, please subscribe my channel, like it, share it and comment it.
Thanking you for watching my video.