Okay, so you know how sometimes we say things are true, like “the sky is blue” or “2+2=4”? Well, sometimes we want to say the opposite of something we said before. It’s kind of like when you say “I’m not hungry” instead of “I’m hungry”.
In computer science, we can do the same thing with a special type of variable called a boolean variable. It can only have one of two values: true or false. So, if we have a boolean variable 𝘈 and it has a value of true, we can use the negation operator “¬” to make its opposite.
The opposite of “true” is “false”, so the negation of 𝘈 would be “false”. We can write this as ¬𝘈 = false.
So, the truth value of ¬𝘈 is false.
Here’s another example to illustrate the concepts of boolean variables:
Okay, so sometimes we have sentences that talk about two things happening together, like “I ate breakfast and then went to school”. We can call these sentences “complex statements”.
In computer science, we can use boolean variables to represent simple statements that are either true or false. But when we have a complex statement with “and” in it, we need to use two boolean variables to represent each part of the statement.
For example, let’s say we have the sentence “It rained today and it was sunny yesterday”. We can represent “It rained today” with a boolean variable called 𝘙 and “It was sunny yesterday” with a boolean variable called 𝘚.
Now, we can use the conjunction operator “∧” to connect the two boolean variables and represent the original sentence as (𝘙 ∧ 𝘚). The conjunction operator takes two boolean variables as input and returns true only if both of them are true.
So, if we know that it did not rain today but it was sunny yesterday, we can say that the value of 𝘙 is false and the value of 𝘚 is true. When we connect them using the conjunction operator, we get (false ∧ true), which is false. So the truth value of (𝘙 ∧ 𝘚) in this case is false.