Now let's begin with negation. If we have a statement P, when you negate that, this will be the symbol. Now take note when you say negation, that means not.
It's a truth value from the statement. For instance, if we assign the truth value for P to be true, then its negation will be false. So it's just the opposite of the truth value of the statement.
If If P is false, its negation is true. So this is the truth table for negation. For conjunction, when you say conjunction, that means and statement. So this is the truth table for conjunction.
So this is only true when both statements are true. So if you notice, it's truth table. This statement here and the conjunction statement. This is only true only when both the statements, the P and Q, are true. If either one of the statements is false or both statements are false, the statement is false.
We have T, T, so P and Q are true. The statement, the conjunction is true. If P is true and Q is false, the statement, this conjunction statement is false.
So if it is false, if P is false and Q is true, the conjunction statement is false. Now if both of these statements are false, then the conjunction statement is also false. So again, to remember this, this is only true when both statements are true. For the disjunction statements, the truth table for a disjunction statement is given by this.
When you say disjunction, this is the or statements. Disjunction statement is only false when both statements are false. So this is, this statement here is always true except for the case when both statements P and Q are false.
So if both statements are true, the OR statement, the disjunction statement is true. If one of the statements is true, just one of the statement is true, then the disjunction statement is true. Well, you could also think of it this way.
It should be both true or just either one of the statement is true for it to be true. Otherwise, if both statements are false, the disjunction statement is also false so in this example we would set p to be the statement this mathematical statement here where 10 is greater than 4 and q represents this mathematical statement 3 less than 5. now both of these statements are true 10 is greater than 4 and 3 is also less than 5. so p is true and q is true now let's determine the truth value for the following statements here so for the first one we have p and q if you recall for conjunction conjunction is only true this is only true if both statements are true now since p is true And this is also true. To determine the truth value for this statement, since both of these statements are true, and for conjunction, if both statements are true, the conjunction is also true. For letter B, we have not P and Q. So if you negate P, if P is said to be true, and you negate it, that becomes false.
So here, this now becomes false. And then you still have a conjunction. For conjunction, if both statements are true, then the statement is true.
Otherwise, the statement is false. Since this one is true and we have a conjunction, one of the statements is false. So therefore, the conjunction here is false. Now, for letter C and letter D, we have a disjunction.
Now, for disjunction, if you remember an OR statement, this is true if either one of the statements or both of the statements are true. So, now let's determine the truth value. Again, this P here is true.
10 is greater than 4. Q is also true. So, if you look at this one, We have P, so that is true, or not Q. Q is true, so not Q is false. You negate it.
P is true, and this not Q is false. So therefore, the disjunction here is true. Since one of the statements here is true, then therefore this statement here is true. Now, if we have not P and then not Q, meaning negate P.
So from true, if you negate that, that becomes false. And then if you negate Q, that would also become false. Now, both of the statements here are false. Therefore, the disjunction statement, the whole statement here is false.