discrete mathematics quiz

1. The composition of two relations RR and SS on a set AA is defined to be S∘R={(x,z):∃ y∈A such that xRy and ySz. Let A={a,b,c,d} and define the relations R={(a,b),(b,c),(d,a)} and S={(a,a),(b,c),(b,d)} on A. Then which of the following ordered pairs are in the composition relation S∘R?

		(a,b),(b,c),(d,a),(a,a) and (b,d) are in the composition relation S∘R.
		(a,a),(d,a) and (b,d) are in the composition relation  S∘R
		(b,c) is in the composition relation S∘R
		(a,c),(d,a) and (a,d) are in the composition relation  S∘R.

6. The matrix below represents a relation RR on the set A×AA×A where A={a,b,c,d,e,f}. There is a 1 in the iith row jjth column if iRj, that is, if (i,j) is in the relation. Otherwise, there is a 0 in the matrix. Which of the following statements is(are) true?