A statement is either true (T) or false (F). “The fish is dead” is a statement, whereas “don’t be dull” is not.
In logic, we have 3 basic connectives; and, or, not. We can use these to make compound statements.
“The fish is dead and you are beautiful.”
“My uncle owns America or you are beautiful.”
“I am not from India and you are not dead.”
Let p and q be statements. Then, to decide the truth value of a compound statement, we could use a truth table:
p q p or q (p v q) p and q (p & q)
T T T T
F T T F
T F T F
F F F F
Does 1=1 AND 2=2? Yes, so (T & T) = T.
But does 1=1 AND 3=4? No, so (T & F) = F.
But does 1=1 OR 3=4? Yes, so (T OR F) = T, and so on.
If you compare this to the truth table of Boolean algebras, you will notice they are equivalent.
You can connect as many statements as you want together to form a compound statement. Two compound statements are equivalent if they have the same truth tables.
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