Set Relation Function Practice session 24.05.2025.pdf

Q.__. Among 100 Students, 32 study Mathematics, 20 study physics, 45 study Biology, 15
study mathematics & Biology, 7 study Mathematics & Physics, 10 study Physics & Biology and
30 do not study any of the three subjects.
(i) Find the number of students studying all three subjects.
(ii) Find the number of students studying exactly one of the three subjects.

Q.__. Let P, Q, R be subsets of a Universal set U.

Q.__. Examine whether relation R on Z is an equivalence relation:

Q.__. Show that the intersection of two equivalence relations is also an equivalence
relation.

Q.__. Let A = {1, 2, 3, 4, 6, 7, 8, 9} and let R be the relation on A X A defined as
(a, b) R (c, d) if a + d = b + c. Prove that R is an equivalence relation.

Q.__. Define Partial Ordering Relation and Equivalence Relation.
Partial Ordering Relation: Let S be a non empty set and ≼ be a relation in S. ≼ is called a
'partially order' if the following three axioms are satisfied:
(i) For any a in S we have a ≼ a (Reflexive)
(ii) If a ≼ b and b ≼ a then a = b (Antisymmetric)
(iii) If a ≼ b and b ≼ c then a ≼ c (Transitive)

Hasse Diagram:
A={1,2,3,4}
R={(1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4), (4,4)}

Q.__. Draw the Hasse diagram for the PO set (A, /) where / stand for divisibility
(i) A = {1, 2, 3, 4, 6, 12}
(ii) A = {2, 3, 6, 12, 24, 36}
(iii) 𝝓, 𝟏 , 𝟐 , 𝟏, 𝟐 , ⊆
(iv) A = {3, 6, 12, 24, 48}

Q.__. Draw the Hasse diagram of the poset (S30, R) where S30 is the set of all positive
divisors of 30 and R is the relation division.

Q.__. Find the domain and range of a function 𝒇 𝒙 =
𝟐𝒙−𝟏
𝒙+𝟒
and then check whether the
function is one-one and onto or not. 2024-25
Q.__. Let f be a function from A to B, where A = B = Set of real numbers R and 𝑓 𝑎 =
2𝑎 − 1
3
. Find f-1

Set Relation Function Practice session 24.05.2025.pdf

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