Samacheer Class 9 Maths - Set Language

(i) The collection of prime numbers up to 100.
✓ Set

(ii) The collection of rich people in India.
✕ Not a set

(iii) The collection of all rivers in India.
✓ Set

(iv) The collection of good Hockey players.
✕ Not a set

(i) INDIA

(ii) PARALLELOGRAM

(iii) MISSISSIPPI

(iv) CZECHOSLOVAKIA

(a) State whether True or False

(i) (18 \in C) → True

(ii) (6 \notin A) → True

(iii) (14 \notin C) → False

(iv) (10 \in B) → True

(v) (5 \in B) → False

(vi) (0 \in B) → False

(b) Fill in the blanks

(i) (3 \in \boxed{A})

(ii) (14 \in \boxed{C})

(iii) (18 \boxed{\notin} B)

(iv) (4 \boxed{\in} B)

(i)

(ii)

or

(iii)

Perfect cubes between 27 and 216 are:

Hence,

(iv)

(i)

(ii)

(iii)

(iv)

(i)

Descriptive Form:
The set of months whose names begin with the letter “J”.

(ii)

Descriptive Form:
The set of prime numbers between 5 and 30.

(iii)

Descriptive Form:
The set of natural numbers less than 5.

(iv)

Descriptive Form:
The set of consonants in the English alphabet.

(i)

(ii)

Values:

(iii)

Values:

(iv)

Elements:

(v)

Leap years between 1882 and 1906:

(i) Set of all districts in Tamil Nadu → Finite

(ii) Set of all straight lines passing through a point → Infinite

(iii)

→ Infinite

(iv)

Roots are (2,3)

→ Finite

(i)

A = vowels in English alphabet

B = letters in “VOWEL”

Both have 5 elements.

✓ Equivalent sets

(ii)

✕ Unequal sets

(iii)

✓ Equal sets

(iv)

Both contain 6 elements.

✓ Equivalent sets

(i)

No natural number exists.

✓ Null set

(ii)

Set of even natural numbers not divisible by 2.

Impossible.

✓ Null set

(iii)

✓ Singleton set

(iv)

Set of triangles having four sides.

Impossible.

✓ Null set

(i)

Common elements:

✓ Overlapping sets

(ii)

C = odd prime numbers greater than 2

D = even prime number

No common element.

✓ Disjoint sets

(iii)

Factors of 24:

Multiples of 3 less than 30:

Common elements:

✓ Overlapping sets

(i) Shapes having 4 equal sides

(ii) Shapes having radius

(iii) Shapes whose interior angles sum to (180^\circ)

(iv) Shapes having 5 sides

Write all subsets.

(i)

(ii)

(iii)

Number of subsets:

(iv)

(i)

Number of subsets:

Proper subsets:

(ii)

Squares:

Subsets:

Proper subsets:

(i)

If (n(A)=4)

(ii)

If (n(A)=0)

(iii)

If

Then,

The Venn diagram is not provided in the question.
So, the elements of the sets cannot be determined exactly.

Generally:

• (i) (A) → all elements inside set (A)
• (ii) (B) → all elements inside set (B)
• (iii) (A \cup B) → elements in (A) or (B) or both
• (iv) (A \cap B) → common elements of (A) and (B)
• (v) (A - B) → elements in (A) but not in (B)
• (vi) (B - A) → elements in (B) but not in (A)
• (vii) (A') → elements not in (A)
• (viii) (B') → elements not in (B)
• (ix) (U) → universal set

(i) (A={2,6,10,14}), (B={2,5,14,16})

Solution

(ii) (A={a,b,c,e,u}), (B={a,e,i,o,u})

Solution

(iii)

Step 1: Write the sets

Solution

(iv)

(A) = set of letters in “mathematics”

(B) = set of letters in “geometry”

Step 1: Write the sets

Solution

Find the following:

(i) (A')

(ii) (B')

(iii) (A' \cup B')

(iv) (A' \cap B')

(v) ((A\cup B)')

Step 1

Therefore,

(vi) ((A\cap B)')

Step 1

Therefore,

(vii) ((A')')

(viii) ((B')')

Find the following:

(i) (A')

(ii) (B')

(iii) (A' \cup B')

(iv) (A' \cap B')

(v) ((A\cup B)')

Step 1

Therefore,

(vi) ((A\cap B)')

Step 1

Therefore,

(vii) ((A')')

(viii) ((B')')

The symmetric difference is:

(i)

Solution

(ii)

Solution

(iii)

Solution

The shaded diagrams are not provided in the question.
Hence the exact expressions cannot be determined.

Common shaded regions are:

| Region | Expression |
| -------------- | ------------ |
| Common part | (A \cap B) |
| Entire portion | (A \cup B) |
| Only A | (A-B) |
| Only B | (B-A) |
| Outside both | ((A\cup B)') |

(i) (A\cup B)

Shade both sets (A) and (B).

(ii) (A\cap B)

Shade only the common overlapping region.

(iii) ((A\cap B)')

Shade every region except the intersection.

(iv) ((B-A)')

Shade everything except the part belonging only to (B).

(v) (A'\cup B')

Shade all regions except the intersection.

(vi) (A'\cap B')

Shade the region outside both sets.

(vii) Observation

From (iii) and (v):

This is one of De Morgan’s Laws.

Find the following:

(i) ((P\cup Q)\cup R)

Step 1: Find (P\cup Q)

Step 2: Find ((P\cup Q)\cup R)

Answer

(ii) ((P\cap Q)\cap S)

Step 1: Find (P\cap Q)

Common elements of (P) and (Q):

Step 2: Find ((P\cap Q)\cap S)

Answer

(iii) ((Q\cap S)\cap R)

Step 1: Find (Q\cap S)

Step 2: Find ((Q\cap S)\cap R)

Answer

Given:

Since every rational number is a real number,

Union

Also,

Therefore,

Hence, the commutative property of union is verified.

Intersection

Also,

Therefore,

Hence, the commutative property of intersection is verified.

Given:

We need to verify:

Left Side

Step 1: Find (A\cup B)

Step 2: Find ((A\cup B)\cup C)

Right Side

Step 1: Find (B\cup C)

Step 2: Find (A\cup(B\cup C))

Conclusion

Hence, the associative property of union is verified.

Given:

We need to verify:

Left Side

Step 1: Find (A\cap B)

Common element:

Step 2: Find ((A\cap B)\cap C)

Right Side

Step 1: Find (B\cap C)

Step 2: Find (A\cap(B\cap C))

Conclusion

Hence, the associative property of intersection is verified.

Given:

Step 1: Write the sets explicitly

Set (A)

Since (n\in W) and (n<4),

Therefore,

Set (B)

Since (n\in N) and (n\le4),

Therefore,

Set (C)

We verify:

Left Side

Step 1: Find (A\cap B)

Step 2: Find ((A\cap B)\cap C)

Right Side

Step 1: Find (B\cap C)

Step 2: Find (A\cap(B\cap C))

Conclusion

Hence, the associative property of intersection is verified.

Given:

Find:

1. (n(A\cap B))
2. (n(U))

Step 1: Find (n(A\cap B))

Using:

Step 2: Find (n(U))

Since:

Answer

Given:

Find:

1. (n(B))
2. (n(U))

Step 1: Find (n(B))

Step 2: Find (n(U))

Answer

Given:

Step 1: Find (n(A))

Step 2: Find (n(B))

Step 3: Find (A\cap B)

Step 4: Find (A\cup B)

Verification

RHS:

LHS:

Thus,

Verified.

Given:

Step 1: Find cardinalities

Step 2: Intersections

Step 3: Union

Verification

RHS:

LHS:

Verified.

Given:

Step 1: Cardinalities

Step 2: Intersections

Step 3: Union

Verification

RHS:

LHS:

Verified.

Given:

• Students in music = 25
• Students in drama = 30
• Students in both = 8

(i) Only music

Answer

(ii) Only drama

Answer

(iii) Total students

Answer

Given:

• Total people = 45
• Tea = 35
• Coffee = 20

Everyone likes tea or coffee or both.

(i) Like both tea and coffee

Answer

(ii) Do not like tea

Answer

(iii) Do not like coffee

Answer

Given:

• 50% passed Mathematics
• 70% passed Science
• 10% failed both
• 300 passed both

Find total students.

Step 1: Passed at least one subject

Since 10% failed both,

passed at least one subject.

Step 2: Let total students = (x)

Mathematics:

Science:

Both:

Using formula:

Answer

students appeared.

Given:

Also,

Step 1: Find (n(A))

Step 2: Find (n(B))

Step 3: Since (n(A)=n(B))

Answer

Given:

• Total investigated = 500
• Car A owners = 400
• Car B owners = 200
• Both A and B = 50

Using formula:

But total people investigated = 500.

This is impossible because total owners cannot exceed total people.

Answer

The data is not correct.