 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that using the given statements, write the conjunction p and q, q and not r and not p and not r. Also determine whether the conjunctions are true or false. Here p is 1 plus 4 equal to 5, q is there are 7 days in a week and r is a correlator has 4 sides. We know that a conjunction is a compound statement which is formed by joining two statements using the connective and. We also know that if both p and q statements are true then their conjunction is also true. If either of p or q is false then their conjunction is also false and if both p and q are false then their conjunction is also false. With this key idea let us proceed with the solution. Here we are given 3 statements p, 1 plus 4 equal to 5, q is there are 7 days in a week and r is a correlator has 4 sides. We will first write p and q. For this we will join the two statements using the connective and. So p and q will be 1 plus 4 equal to 5 and there are 7 days in a week. Now we determine whether it is true or false. Here we see that the statement p that is 1 plus 4 equal to 5 and the statement q that is there are 7 days in a week are true statements. So as we know from the key idea if both p and q statements are true then their conjunction is also true. This implies that p and q is also a true statement. Now we write q and not r. We have the statement q is there are 7 days in a week and the statement r is a correlator has 4 sides. To write q and not r we first write negation of r. So not r will be a correlator does not have 4 sides. So q and not r will be there are 7 days in a week and a correlator does not have 4 sides. Now we determine whether this statement is true or false. Here q is there are 7 days in a week which is a true statement and not r is a correlator does not have 4 sides which is a false statement. As we know from the key idea if either of p or q is false then the conjunction is also false. This implies q and not r is a false statement. Now we write not p and not r. As we know p is 1 plus 4 equal to 5 and r is a correlator has 4 sides. So not p is 1 plus 4 is not equal to 5 and not r is a quadrilateral does not have 4 sides. So not p and not r is 1 plus 4 is not equal to 5 and a quadrilateral does not have 4 sides. Now we determine whether this statement is true or false. The statements not p that is 1 plus 4 not equal to 5 and not r that is a quadrilateral does not have 4 sides are false statements. As we know from the key idea if both p and q are false then their conjunction is also false. This implies not p and not r is a false statement. This is the required answer. With this we complete our session. Hope you enjoyed the session.