 Hello and welcome to the session. The question says, find the following statement in five different ways conveying the same meaning. The given statement is, if a triangle is equiangular then it is an obtuse angle triangle. So, first let us learn the implications of statements with if and then. Now here the given statement has if also and then also. So, the implications of statements with if and then are first, p implies q if p and q are two component statements which form a compound statement with the help of connecting word. Second is, p is sufficient condition for q. Third is, p only if q. Fourth is, q is a necessary condition for p and the fifth one is not q implies not p. So, this is the key idea we are going to use in this problem to write the given statement in five different ways. Let us now start with the solution and first let us write the component statements of this compound statement. Now it is component statements, let us note the component statements by p1 and q. Now the first statement is a triangle is, sorry, equiangular and the second statement is triangle, angle, triangle. The implication of this statement with if and then is p implies q. So, here the component statements are p1 and q. So, we have p1 implies q. Thus the first statement is a triangle is equiangular implies it is an obtuse angle triangle. The second implication is p is sufficient condition for q. That is p1 is sufficient condition for p, sorry q. So, the second statement is for the triangle to be an obtuse angle triangle sufficient that it is equiangular. Now the third implication is p only fq. So, the third will be a triangle, equiangular, obtuse angle triangle. Now let us see the fourth implication. Here this q is a necessary condition for p. So, here we will have q is a necessary condition for p1. Thus the fourth statement is for the triangle to be an obtuse angle triangle necessary the triangle is equiangular. Let us see the fifth implication which says not q implies not p that is not q implies not p1 here. So, the fifth statement is if a triangle is not an obtuse angle triangle it is not equiangular. So, these are the five statements which convey the same meaning as the given statement p. So, this completes the session. Hope you have understood it well. Take care and have a good day.