1. Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A?
2. Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true?
Every non-empty subset of has a greatest lower bound
3. Let S be a set of n>0 elements. Let be the number Brof binary relations on S and let Bf be the number of functions from S to S. The expression for Br and Bf, in terms of n should be _
4. Let R1 and R2 be two equivalence relations on a set. Is R1 ∪ R2 an equivalence relation?
an equivalence relation
5. What the condition for a binary relationship to be symmetrical?
6. The inclusion of _ sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.
7. Determine the characteristics of the relation aRb if a2= b2
8. The number of equivalence relations of the set {3, 6, 9, 12, 18} is _
9. how many binary relations are there on a set S with 8 distinct elements?
10. The condition for a binary relaton to be symmetric is –
11 Let R1 and R2 be two equivalence relations on a set. Is R1 ∪ R2 an equivalence relation?
an equivalence relation
13 The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {1, 2, 3, 4, 5} is __
14 The binary relation U = Φ (empty set) on a set A = {13, 23,31} is –
15 The less-than relation, <, on a set of real numbers is –
16 What is the number of hasse diagram –
17 - number of reflexive closure exists in a relation R = {(0,1), (1,1), (1,3), (2,1), (2,2), (3,0)} ?
18 A relation R is defined on the set of integers as aRb if and only if a+b is even and R is termed as __
19 give examples of the number of reflex closures ?
20 Give an example of the transit closure of both relationships ?
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