 Hi and how are you all today? Let us discuss the following question it states. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. So first of all you need to tell whether the statements are true and false and if it is a false statement we need to rewrite the correct statement. So let us start with our first statement. It says if p is equal to elements m and n and q are having elements n and m then p cross q is equal to mn the ordered pairs mn and nm. So this is a false statement and the reason is that if we need to find out p cross q the ordered pair will be such that the first element of the ordered pair belongs to p and the other belongs to q. So m with n will be the first ordered pair then m with m will be another ordered pair n with n will also be another ordered pair and then n with m. So this is the correct statement, right? So proceeding on to the second part. It says if a and b are non-empty sets then e cross b is a non-empty set of ordered pair xy such that x belongs to a and y belongs to b. This is a true statement because we know that if a and b are non-empty set and let us have their elements as 2, 3 let's say. And if we need to find out a cross b the elements of a cross b will be 2, 3 and this is also a non-empty set where x belongs to a and y belongs to b. So that is why this is a true statement. Proceeding on with the last and final part it says if a is equal to 1, 2 and b is equal to 3, 4 then e cross b intersection phi is equal to phi. Now let us find out its answer and then we will be able to tell whether this is a true or false statement. So a cross first of all we need to find out b intersection phi. It will be the elements 3, 4 intersection phi and the answer will be phi, right? And now a cross b intersection phi will be ordered pairs 1, 2 cross phi. Now we can write in place of b intersection phi the answer that we obtained phi and hence our answer will always be equal to phi again. That means this is a true statement. So we were able to justify our answers also and this helped in making our vision more clearer. Bye for now.