Write the set of letters of the following words in Roster form
PRINCIPAL

Are P = { x : –3 ≤ x ≤ 0, x ∈ Z} and Q = The set of all prime factors of 210, equivalent sets?

Write all the subsets of A = {a, b}.

Draw Venn diagram and shade the region representing the following sets
(i) A′

If n(A) = 36, n(B) = 10, n(A∪B) = 40, and n(A′) = 27 find n(U) and n(A∩B).

Which of the following are sets?
The Collection of good Hockey players.

List the set of letters of the following words in Roster form.
PARALLELOGRAM

Represent the following sets in descriptive form.
Q = {7,11,13,17,19,23,29}

Represent the following sets in descriptive form
S = {x : x is a consonant in English alphabets}

Which of the following sets are equivalent or unequal or equal sets?
X = The set of A = { x : x is a letter in the word “LIFE”}
Y = {F, I, L, E}

Identify the following sets as null set or singleton set.
A = {x : x ∈ N, 1 < x < 2}

Write down the power set of the following sets.
E = ∅

Find the number of subsets and the number of proper subsets of the following sets.
X = { x² : x ∈ N, x² ≤ 100}.

Using the given Venn diagram, write the elements of A∪B

Find A∪B, A∩B, A–B and B–A for the following sets.
A = Set of all letters in the word “mathematics” and
B = Set of all letters in the word “geometry”

If U = {a, b, c, d, e, f, g, h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets. A′\(\cup \) B′

Find the symmetric difference between the following sets. R = {l, m, n, o, p} and S = {j, l, n, q}

Using the set symbols, write down the expressions for the shaded region in the following.

If A =\(\left\{ -\frac { 1 }{ 2 } ,0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2 \right\} \), B =\(\left\{ 0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2,\frac { 5 }{ 2 } \right\} \) and C =\(\left\{ -\frac { 1 }{ 2 } .\frac { 1 }{ 4 } ,1,2,\frac { 5 }{ 2 } \right\} \), then verify \(A\cap (B\cap C)=(A\cap B)\cap C\) .

Verify the associative property of intersection of sets for A =\(\{ -11,\sqrt { 2 } ,\sqrt { 5 } ,7\} \), B =  \(\\ \{ \sqrt { 3 } ,\sqrt { 5 } ,6,13\} \) and C = \(\{ \sqrt { 2 } ,\sqrt { 3 } ,\sqrt { 5 } ,9\} \).

Use a fractional index to write: \(\sqrt{5}\)

Rationalise the denominator
(i) \(\frac { 1 }{ \sqrt { 50 } } \)
(ii) \(\frac { 5 }{ 3\sqrt { 5 } } \)
(iii) \(\frac { \sqrt { 75 } }{ \sqrt { 18 } } \)
(iv) \(\frac { 3\sqrt { 5 } }{ \sqrt { 6 } } \)

(a)

(i) \(\frac { \sqrt { 2 } }{ 10 } \)
(ii) \(\frac { \sqrt { 5 } }{ 3 } \)
(iii) \(\frac { 5\sqrt { 6 } }{ 6 } \)
(iv) \(\frac { \sqrt { 30 } }{ 2 } \)

Write the following numbers in decimal form:
6.34 \(\times\)10⁴

Find the value of the polynomial f (y) =  6y - 3y² + 3 at y = 1

Expand the following using identities: (3x + 4y)²