PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

State whether the following statements are true or false: 

\[1 \in \left\{ 1, 2, 3 \right\}\]

State whether the following statements are true or false: 

\[a \subset {b, c, a}\] 

State whether the following statements are true or false: 

\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]

State whether the following statements are true or false: 

\[\left\{ a, b \right\} = \left\{ a, a, b, b, a \right\}\] 

State whether the following statements are true or false:

The set {x ; x + 8 = 8} is the null set. 

Decide among the following sets, which are subsets of which:

\[A = {x : x \text{ satisfies } x^2 - 8x + 12 = 0},\]

\[B = \left\{ 2, 4, 6 \right\}, C = \left\{ 2, 4, 6, 8, . . . \right\}, D = \left\{ 6 \right\} .\]

Write which of the following statements are true? Justify your answer. 

The set of all integers is contained in the set of all set of all rational numbers. 

Write which of the following statement are true? Justify your answer. 

The set of all crows is contained in the set of all birds. 

Write which of the following statement are true? Justify your answer. 

 The set of all rectangle is contained in the set of all squares.

Write which of the following statement are true? Justify your answer.

 The set of all real numbers is contained in the set of all complex numbers.

Write which of the following statement are true? Justify your answer.

The sets P = {a} and B = {{a}} are equal.

Write which of the following statement are true? Justify your answer. 

The sets A = {x : x is a letter of the word "LITTLE"} and,B = {x : x is a letter of the word "TITLE"} are equal. 

Let A = {a, b, {c, d}, e}. Which of the following statement are false and why? 

\[a \subset A\]

Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?

\[\left\{ a, b, e \right\} \subset A\] 

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?\[\left\{ 2 \left\{ 1 \right\} \right\} \not\subset A\] 

Write down all possible subsets of each of the following set:

\[\left\{ \phi \right\}\]

Find the conjugate of the following complex number:

4 − 5 i

Find the conjugate of the following complex number:

\[\frac{1}{3 + 5i}\]

Find the conjugate of the following complex number:

\[\frac{1}{1 + i}\]