Solve the Following Question.(2 Marks)

Question 12 Marks

In a school, there are 20 teachers who teach Mathematics or Physics. of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?

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Question 22 Marks

In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?

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Question 32 Marks

Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b) / a ∈ A, b ∈ B, a – b is an even number}.
Show that R is an empty relation from A to B.

Answer

A= {6, 8}, B = {1, 3, 5}
R = {(a, b)/ a ∈ A, b ∈ B, a – b is an even number}
a ∈ A
∴ a = 6, 8
b ∈ B
∴ b = 1, 3, 5
When a = 6 and b = 1, a – b = 5 which is odd
When a = 6 and b = 3, a – b = 3 which is odd
When a = 6 and b = 5, a – b = 1 which is odd
When a = 8 and b = 1, a – b = 7 which is odd
When a = 8 and b = 3, a – b = 5 which is odd
When a = 8 and b = 5, a – b = 3 which is odd
Thus, no set of values of a and b gives a – b even.
∴ R is an empty relation from A to B.

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Question 42 Marks

Express $\left\{(x, y) / x^2+y^2=100\right.$, where $\left.x, y \in W\right\}$ as a set of ordered pairs.

Answer

$
\left\{(x, y) / x^2+y^2=100, \text { where } x, y \in W\right\}
$
We have, $x^2+y^2=100$
When $x=0$ and $y=10$,
$
x^2+y^2=0^2+10^2=100
$
When $x=6$ andy $=8$,
$
x^2+y^2=6^2+8^2=100
$
When $x=8$ and $y=6$,
$
x^2+y^2=8^2+6^2=100
$
When $x =10$ and $y =0$,
$
x^2+y^2=10^2+0^2=100
$
$\therefore$ Set of ordered pairs $=\{(0,10),(6,8),(8,6),(10,0)\}$

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Question 52 Marks

In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take both tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes atleast one beverage, find the number of students in the hostel.

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Question 62 Marks

If $A, B, C$ are the sets for the letters in the words 'college', 'marriage' and 'luggage' respectively, then verify that $[A-(B \cup C)]=[(A-B) \cap(A-C)]$.

Answer

A = {c, o, l, g, e}
B = {m, a, r, i, g, e}
C = {l, u, g, a, e}
B ∪ C = {m, a, r, i, g, e, l, u}
A – (B ∪ C) = {c, o}
A – B = {c, o, l}
A – C = {c, o}
∴ [(A – B) ∩ (A – C)] = {c, o} = A – (B ∪ C)
∴ [A – (B ∪ C)] = [(A – B) ∩ (A – C)]

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Maths (commerce) Solve the Following Question.(2 Marks)

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