Logic is a big deal when it comes to using math to figure things out.
In this logic world, we work with propositions, which are just sentences that can be either true or false but not both at the same time. It’s like saying something is either right or wrong – no in-between.
Think of it like using 1 for true and 0 for false in the digital world.
Examples of Propositions
"An elephant is larger than a cat."
- Is this a statement? Yes.
- Is this a proposition? Yes.
- What is the truth value of this proposition? True.
"1089 < 101"
- Is this a statement? Yes.
- Is this a proposition? Yes.
- What is the truth value of this proposition? False.
"y > 15"
- Is this a statement? Yes.
- Is this a proposition? No.
Explanation: The truth value depends on the y value, the y value is not specified. This type of statement is an open sentence.
"This month is February and 24 < 5."
- Is this a statement? Yes.
- Is this a proposition? Yes.
- What is the truth value of this proposition? False.
Explanation: The conjunction “February and 24 < 5” is false because it combines a true statement (the month is February) with a false statement (24 is not less than 5).
"Hand over your money now!"
- Is this a statement? No.
- Is this a proposition? No.
Explanation: Only statements can be proposition.
When constructing logical arguments, it’s often necessary to combine propositions using various logical operators such as conjunction (AND), disjunction (OR), and negation (NOT). These operators allow us to form more complex statements by linking together simpler propositions. Check out Combining Propositions.