C-01 — Set and Function

What is a set?

The set $S = \{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\}$ represents which of the following?

The method of expressing a set by listing its elements between braces is called:

The set $S = \{x : x$ is a square number not greater than $100\}$ uses which method?

If $x$ is an element of set $A$, the correct notation is:

If $x$ is not an element of set $A$, the correct notation is:

A particular set is called the universal set when:

For the sets $S = \{x : x$ is a positive integer and $x^2 < 16\}$, $T = \{x : x$ is a positive integer and $x^2 < 20\}$, $P = \{x : x$ is a positive integer and $\sqrt{x} < 2\}$, the universal set $U$ may be taken as:

The symbol $\mathbb{N}$ denotes the set of all:

The symbol $\mathbb{Z}$ denotes the set of all:

$\mathbb{Q}$ is the set of all:

$\mathbb{R}$ denotes the set of all:

Consider the following statements:

$A \subset B$ means:

If $A = \{2, 3\}$ and $B = \{2, 3, 5, 7\}$, then:

Which of the following is true for $A = \{1, 3\}$ and $B = \{2, 3, 5, 7\}$?

If $A = \{x : x$ is a positive integer$\}$, $B = \{0\}$ and $X = \{x : x$ is an integer$\}$, which of the following is correct?

The empty set is denoted by:

The set $\{x : x$ is a real number and $x^2 < 0\}$ is:

The number of elements in the empty set is:

The set $F = \{x : x$ is an African country that won the FIFA world cup till 2014$\}$ is:

Two sets $A$ and $B$ are equal if and only if:

For $A = \{1, 2, 3, 4\}$ and $B = \{1, 2, 2, 3, 4, 4, 4\}$:

$A$ is a proper subset of $B$ if and only if:

Consider the following statements:

$A \setminus B$ is defined as:

If $A = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ and $B = \{0, 2, 4, 6, 8, 10\}$, then $A \setminus B$ = ?

Which of the following is always true?

If $U$ is the universal set and $A \subset U$, the complement of $A$ is:

The complement of $A$ is denoted by:

If $U$ is the set of all integers and $A$ is the set of all negative integers, then $A'$ = ?

The power set $P(A)$ is:

$P(\emptyset)$ = ?

If $A = \{a\}$, then $P(A)$ = ?

Number of elements in $P(\{a, b\})$:

Number of elements in $P(\{a, b, c\})$:

If $|A| = n$, then $|P(A)|$ = ?

If $A = \{a, b\}$ and $B = \{b, c\}$, which is correct?

The Venn diagram is named after:

$A \cup B$ = ?

$A \cap B$ = ?

With $U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$, $A = \{x : x$ prime in $U\}$, $B = \{x : x$ odd in $U\}$, then $A \cap B$ = ?

Same example: $A \cup B$ = ?

Same example: $A'$ = ?

Same example: $(A \cup B)'$ = ?

Same example: $(A \cap B)'$ = ?

Sets $A$ and $B$ are called disjoint if:

If $A = \{x : x$ positive integer$\}$ and $B = \{x : x$ negative integer$\}$, then $A$ and $B$ are:

The Cartesian product $A \times B$ is:

If $A = \{1, 2\}$ and $B = \{a, b, c\}$, then number of elements in $A \times B$ is:

If $|A| = 4$ and $|B| = 5$, then $|A \times B|$ = ?

Commutative law states $A \cup B$ = ?

Associative law states $(A \cup B) \cup C$ = ?

Distributive law: $A \cup (B \cap C)$ = ?

Distributive law: $A \cap (B \cup C)$ = ?

De Morgan's law: $(A \cup B)'$ = ?

De Morgan's law: $(A \cap B)'$ = ?

$A \cup A$ = ?

$A \cup \emptyset$ = ?

$A \cap \emptyset$ = ?

$A \cup U$ = ?

$A \cap U$ = ?

If $A \subset B$, then:

If $A \subset B$, then $A \cup B$ = ?

If $A \subset B$, then $A \cap B$ = ?

$A \setminus B$ is also equal to:

Consider the following statements:

A matching where each element of $A$ corresponds to a unique element of $B$ and vice versa is called:

Sets $A$ and $B$ are equivalent if:

Equivalent sets are denoted by:

Consider the following properties of equivalence:

The sets $A = \{1, 2, 3, \ldots, n\}$ and $B = \{1, 3, 5, \ldots, 2n-1\}$ are:

$(a, b) = \{x \in \mathbb{R} : a < x < b\}$ is called:

$[a, b]$ denotes:

$[a, b)$ represents:

$(a, b]$ is called:

A set whose elements can be fixed by counting is called:

The number of elements in a finite set $A$ is denoted by:

The set of natural numbers $\mathbb{N}$ is:

A set $A$ is infinite if and only if:

The number of elements in the empty set is:

If $A$ and $B$ are disjoint finite sets, then $n(A \cup B)$ = ?

For any finite sets $A$ and $B$, $n(A \cup B)$ = ?

$n(A \cup B \cup C)$ = ?

Out of 50 persons, 35 can speak English, 25 can speak both English and Bangla, and everyone speaks at least one of the two languages. How many can speak Bangla?

In the above problem, how many can speak only Bangla?

Among 35 girls, each likes at least one of running, swimming, dancing. 15 like running, 4 like all three, 2 like only running, 7 like running and swimming but not dancing, $x$ like swimming and dancing but not running, $2x$ like only dancing, 2 like only swimming. The value of $x$ is:

In the above problem, the number of girls who like running and dancing but not swimming is:

Out of 24 students, 18 like basketball, 12 like volleyball. If $x = n(B \cap V)$, the minimum value of $x$ is:

In the above problem, the maximum value of $x$ is:

In a class of 30 students, 20 like football and 15 like chess. Every student likes at least one of the two games. How many students like both?

Among some persons, 50 speak Bangla, 20 speak English, 10 speak both. How many of these speak at least one of the two?

Out of 100 students, 42 took French, 30 took German, 28 took Spanish, 10 took French and Spanish, 8 took German and Spanish, 5 took German and French, 3 took all three. How many took none?

In the above problem, how many took just one of the three languages?

Same problem: how many took only two of the three?

Out of 50 science students, 29 took Biology, 24 took Higher Mathematics, 11 took both. How many took neither?

Consider the following statements:

Let $A_n = \{n, 2n, 3n, \ldots\}$ for every $n \in \mathbb{N}$. Then $A_2 \cap A_3$ = ?

With $A_n$ as above, $A_3 \cap A_6$ = ?

With $A_n$ as above, $A_2 \cap A_4$ = ?

Given $U = \{x : 1 \leq x \leq 20,\ x \in \mathbb{Z}\}$, $A = \{x : x$ odd$\}$, $B = \{x : x$ prime$\}$. Then $C = A \cap B$ = ?