Binary-04-Assignment

1. Let S be a finite set containing n elements. Then the total number of commutative binary operations on S is (a) (b) (c) (d) 2. If S is a finite set having n elements, then the total number of non-commutative binary operation on S is (a) (b) (c) (d) 3. If the composition table for a binary operation * defined on a set S is symmetric about the leading diagonal, then (a) * is associative on S (b) * is commutative on S (c) S has the identity element for * (d) None of these 4. Subtraction of integers is an operation that is (a) Commutative and associative (b) Not commutative but associative (c) Neither commutative nor associative (d) Commutative but not associative 5. The law is called (a) Closure law (b) Associative law (c) Commutative law (d) Distributive law 6. If any one of the rows of the composition table for a binary operation * on a set S coincides with the top most row of the table, then (a) S has a left identity for * (b) S has a right identity for * (c) S has the identity element for * (d) * is commutative and associative on S 7. If any one of the columns of the composition table for a binary operation * on a set S coincides with the left most column of the table, then (a) S has a left identity for * (b) S has a right identity for * (c) S has the identity element for * (d) * is commutative and associative on S 8. Which of the following binary operations is commutative (a) * on R, given by (b) O on R, given by (c) on P(S), the power set of a set S given by (d) None of these

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