Distributive Property

Q.

Let $A$ and $B$ be two sets then $\left(A\cup B\right)\cup \left(A\cap B\right)$

1. $A$

2. $A$

3. $B$

4. None of these

Q.

Let $p$ be a prime number such that $p\ge 3$. Let $x=p!+1$. The number of primes in the list $n+1,n+2,n+3,....,n+p–1$ is

1. $p-1$

2. $2$

3. $1$

4. $0$

Q.

Question 101 (iii)

Here is keyboard of a harmonium.

This pattern of keys is repeated on a larger keyboard. How many black keys would you expect to find on a keyboard with 14 such patterns?

Q.

A survey shows that $63\%$ of the Americans like cheese whereas $76\%$ like apples.

If $x\%$ of the Americans like both cheese and apples, then

1. $x=39$

2. $x=63$

3. $39\le x\le 63$

4. None of these

Q.

Factorise 10pq + 9 + 6p + 15q and give the value of the expression for p = 3 and q = 2 [3 MARKS]

Q.

In a hospital, $89\%$ has the disease $A$ and $98\%$ has the disease $B$, $K\%$ is the number of patients who has both, then $K$ cant be the subset of

Q.

If $AandB$ are two disjoint sets, then which one of the following is correct?

1. $A-B=A-(A\cap B)$

2. $B-A=A\cap B$

3. $A\cap B=(A\cup B)$

4. none of these

Q. If $A$ and $B$ are disjoint sets, then $n(A\cup B)$ is

1. $n\left(A\right)+n\left(B\right)$
2. $n\left(A\right)\times n\left(B\right)$
3. $\sqrt{n\left(A\right)\cdot n\left(B\right)}$
4. $\frac{n\left(A\right)+n\left(B\right)}{2}$

Q. Show that for any sets $A$ and $B$,
$A=(A\cap B)\cup (A–B)$ and $A\cup (B–A)=(A\cup B)$.

Q.

Question 125 (i)

If '*' is an operation have, such that for integers a and b. We have
$a\ast b=a\times b+(a\times a+b\times b),$ then find
$(-3)\ast (-5)$

Q. If $A=\{1,2,3\},B=\{2,4,5\}$ and $C=\{4,1,9\},$ then $A\cap (B\cup C)$= ___.

1. $(A\cap B)\cup (A\cap C)$
2. $(A\cup B)\cap (A\cup C)$
3. $(A\cap B)\cup C$
4. $\{1,2\}$

Q. If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B ={2, 4, ......, 18} and N, the set of natural numbers is the universal set, then $(A^{\prime }\cup [(A\cup B)\cap B^{\prime }\left]\right)$ is

1. N
2. $\varphi$
3. B
4. A

Q. Given : ${\log }_{3}m=x$ and ${\log }_{3}n=y$

Q. If $n\left(A\right)=10,n\left(B\right)=12$ and $n(A\cap B)=6$ then find $n(A\cup B)$

Q. If $A=\{1,2,3\},B=\{2,4,5\}$ and $C=\{4,1,9\},$ then $A\cup (B\cap C)$= ___.

1. $(A\cup B)\cap (A\cup C)$
2. $(A\cap B)\cup (A\cap C)$
3. $\{1,2,3,4\}$
4. $(A\cup B)\cap C$

Q.

Let $n(A-B)$ = $25+x$, $n(B-A)$ = $2x$ and $n(A\cap B)$ = $2x$. If n(A) = 2(n(B)) then the value of 'x' is ___.

Q. $k(A+B)=kA+kB$ is called ..........law.

1. distributive
2. commutative
3. both (a) and (b) above
4. none of the above

Q.

Represent 32.73737373737373…… in a rational form.

Q.

835 x 105 using distributive property over addition for multiplication to simplify

Q.

1. $A\cap B=\left\{3\right\}$
2. $A\cup B=\left\{3\right\}$
3. None of the above
4. $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$

Q. For A={x|x is a prime factor of 24}, B=(x|5 < x $\le$ 12, x $ϵ$ N) and C= { 1, 4, 5, 6}

Q. Let $A=\{1,2,3\},B=\{3,4\}$ and $C=\{4,5,6\}$. Find
$A\times (B\cup C)$

Q. State whether the given statement is true or false:

1. True
2. False

Q. Show that $A-(A-B)=$ $\varphi \cup (A\cap B)=A\cap B$

Q. Which of the following represent the distributive law in sets?

1. $A\cup (B\cap C)=(A\cap B)\cup (A\cap C)$
2. $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$
3. $A\cap (B\cup C)=(A\cup B)\cap (A\cup C)$
4. $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$

Q. Let $U=\{-2,-1,0,1,2,3,....,10\},A=\{-2,2,3,4,5\}$ and $B=\{1,3,5,8,9\}$. Verify De Morgan's laws of complementation

Q. Is ${}^{\prime }{\ast }^{\prime }$ defined on the set {1, 2, 3, 4, 5} by $a\ast b$ = LCM of a and b, a binary operation ? Justify your answer.

Q. Let $A,B$ be two disjoint sets then $A\cap (A^{\prime }\cup B)=$

Q.

Deepak scored $35$ out of $40$ in a mental Maths Drill and $78$ out of $90$ in his Science Drill. Calculate the percentage he score in both the subject. In which subject did he performed better?

Q. If $n\left(A\right)=15,n(A-B)=10$ then find $n(A\cap B)$