Logical implication
Master Logical implication in Grade 10 math. ### Property An 'if-then' statement, written as , means ' implies '. The entire statement is conside. Practice with Saxon Algebra 2 examples.
Key Concepts
Property An 'if then' statement, written as $p \to q$, means '$p$ implies $q$'. The entire statement is considered true in all cases except one: it is only false when the first part, $p$, is true and the second part, $q$, is false.
Example 1: Statement 'If a creature is a spider ($p$), then it has eight legs ($q$)' is $p \to q$. This is only false if you find a spider that does not have eight legs. Example 2: Statement 'If you get an A on the test ($p$), we will celebrate ($q$)' is $p \to q$. The promise is only broken if you get an A and we do not celebrate.
Think of this as a one way promise. The statement 'if p, then q' only breaks if the first part (p) happens but the promised second part (q) doesn't. For example, 'If you clean your room, I'll give you ten dollars.' The only way I've lied is if you actually clean your room and I don't pay up.
Common Questions
What is Logical implication?
### Property An 'if-then' statement, written as , means ' implies '. The entire statement is considered true in all cases except one: it is only false when the first part, , is true and the second part, , is false. Logical implication is just a fancy term for an 'if-then' statement, like a...
How do you apply Logical implication in practice?
Example 1: Statement 'If a creature is a spider (), then it has eight legs ()' is . This is only false if you find a spider that does not have eight legs. Example 2: Statement 'If you get an A on the test (), we will celebrate ()' is . The promise is only broken if you get an A and we do not...
Why is Logical implication important for Grade 10 students?
Think of a logical implication, , like a simple promise. For example: 'If you finish your homework (), then we can watch a movie ().' The only way this promise is broken is if you finish your homework, but we don't watch a movie. Here’s when the promise holds true or is broken: Homework done (...