Biconditionals
- Intro Lesson8:00
- Lesson: 1a2:19
- Lesson: 1b2:19
- Lesson: 1c2:14
- Lesson: 2a4:48
- Lesson: 2b2:45
- Lesson: 2c3:08
- Lesson: 3a13:22
- Lesson: 3b8:14
- Lesson: 3c6:28
- Lesson: 3d6:42
- Lesson: 4a9:01
- Lesson: 4b5:57
- Lesson: 4c5:30
- Lesson: 4d5:29
Biconditionals
Lessons
A biconditional is a conjunction of a conditional and its converse. In symbolic form it would be:
(p→q) ˄ (q→p)
We can also write it as p↔q. In words, we connect p and q with "if and only if". A biconditional can be only true if both the conditional and converse is true. Here is a truth table of a biconditional.
p | q | p→q | q→p | (p→q) ˄ (q→p) | p↔q |
T | T | T | T | T | T |
T | F | F | T | F | F |
F | T | T | F | F | F |
F | F | T | T | T | T |
- IntroductionBiconditionals Overview:a)What are Biconditionals
- 1.Forming the Biconditional
Write a biconditional using the given conditionals:a)If today is Monday, then yesterday was Sunday.
If yesterday was Sunday, then today is Mondayb)If he drives faster than 100 km, then he will get a ticket.
If he gets a ticket, then he has driven faster than 100 km.c)If today is the weekend, then I do not go to school.
If I do not go to school, then it is the weekend. - 2.You are given 3 statements in symbolic form:
p: There is cream in milk
q: There is milk in coffee
r: There is cream in coffeea)Write the conditional (p ˄ q) → r in words.b)Write the converse(p ˄ q) → r in words.c)Write the biconditional. - 3.Truth value of Biconditionals
Determine the truth value of the following biconditionals:a)x=5. if and only if x+7=12.b)If x>5, if and only if x>2.c)The triangle is an isosceles, if and only if two sides are equal.d)The angle is acute, if and only if the angle is less than 90° degrees. - 4.Let both p, q and r be statements.a)If p is true, q is true and r is false, then what is the truth value of the biconditional (p ˄ q) ↔r ?b)If p is false, q is true and r is false, then what is the truth value of the biconditional (p ˄ q) ↔r ?c)If p is false, q is false and r is true, then what is the truth value of the biconditional (p ˄ q) ↔r ?d)If p is false, q is false and r is false, then what is the truth value of the biconditional (p ˄ q) ↔r ?