# For any 3 sets A, B and C, prove that : <br> (i) `A-(B cupC)=(A-B)cap(A-C)` <br> (ii) `A-(BcapC)=(A-B)cup(A-C)` <br> (iii) `A cap(B-C)= (A cap B) - (A cap C)` <br> (iv) `(A cupB)-C=(A-C)cup(B-C)` <br> (v) `A cap (B DeltaC)=(A capB)Delta(A capC)`.

Updated On: 10-9-2020

58.8 k+

28.6 k+

Answer

Text Solution

(i)

A-(BcupC)

<br>

=Acap(BcupC)'" "(becauseX-Y=X capY')

<br>

=Acap(B'capC')=(AcapB')cap(A capC)

<br>

=(A-B)cap(A-C)

. <br> (ii)

A-(BcapC)

<br>

=Acap(BcapC)'

<br>

=A cap(B'cupC')

<br>

= (A cap B')cup (A cap C')

(From distributive law) <br>

= (A-B) cup (A-C)

. <br> (iii)

A cap(B-C)

<br>

=A cap(BcapC')" "(becauseX-Y=XcapY')

<br>

=(AcapB)capC'

(From associative law) <br> <br>

= phicup[(AcapB)capC']

<br>

=[(AcapB)capA']cup[(AcapB)capC']

<br>

=(A capB)cap (A' cup C')

(From distributive law) <br>

=(AcapB)cap(AcapC)'

<br>

=(AcapB)-(A capC)" "(because XcapY'=X-Y)

<br> (iv)

(A cupB)-C

<br>

=(A cup B)capC'" "(X-Y=X capY')

<br>

=(A capC')cup (B cap C')

(From distributive law) <br>

= (A-C)cup(B-C)" "(becauseX capY'=X-Y)

<br> (v)

A cap(B DeltaC)

<br>

=A cap[(B-C)cup(C-B)]

<br>

[Acap(B-C)]cup[Acap(C-B)]

(From distributive law) <br>

= [(A capB)-(AcapC)]cup[(AcapC)-(AcapB)]

<br>

=(A capB)Delta(AcapC)

.

Related Videos

View AllVery Important Questions

Let

f(x)=ax^2-bx+c^2, b != 0

and

f(x) != 0

for all

x ∈ R

. Then (a)

a+c^2 < b

(b)

4a+c^2 > 2b

(c)

a-3b+c^2 < 0

(d) none of these

When an

AC

signal of frequency

1 kHz

is applied across a coil of resistance

100 Omega

, then the applied voltage leads the current by

45^@

. The inductance of the coil is

The median of the data is 10 (b) 11 9 (d) None of these

The point on the curve

y=12 x-x^2

where the slope of the tangent is zero will be

(0,\ 0)

(b)

(2,\ 16)

(c)

(3,\ 9)

(d)

(6,\ 36)

An electron in H-atom in its ground state absorbs

1.5

times as much energy as the minimum required for its escape ( i. e., 13 . 6 eV) from the atom . Calculate the wavelength of emitted electron.

Space is divided by the line AD into two regions. Region I is field free and the Region II has a unifrom magnetic field B direction into the plane of the paper. ACD is a simicircular conducting loop of radius r with center at O, hte plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity

omega

about an axis passing through O and the perpendicular to the plane of the paper. The effective resistance of the loop is R. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/JMA_EIA_C15_038_Q01.png" width="80%"> <br> (i) obtain an expression for hte magnitude of the induced cureent in the loop. <br> (ii) Show the direction of the current when the loop is entering into the Rigion II. <br> Plot a graph between the induced e.m.f and the time of roation for two periods or rotation.

Space is divided by the line AD into two regions. Region I is field free and the Region II has a unifrom magnetic field B direction into the plane of the paper. ACD is a simicircular conducting loop of radius r with center at O, hte plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity

omega

about an axis passing through O and the perpendicular to the plane of the paper. The effective resistance of the loop is R. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/JMA_EIA_C15_038_Q01.png" width="80%"> <br> (i) obtain an expression for hte magnitude of the induced cureent in the loop. <br> (ii) Show the direction of the current when the loop is entering into the Rigion II. <br> Plot a graph between the induced e.m.f and the time of roation for two periods or rotation.

Space is divided by the line AD into two regions. Region I is field free and the Region II has a unifrom magnetic field B direction into the plane of the paper. ACD is a simicircular conducting loop of radius r with center at O, hte plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity

omega

about an axis passing through O and the perpendicular to the plane of the paper. The effective resistance of the loop is R. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/JMA_EIA_C15_038_Q01.png" width="80%"> <br> (i) obtain an expression for hte magnitude of the induced cureent in the loop. <br> (ii) Show the direction of the current when the loop is entering into the Rigion II. <br> Plot a graph between the induced e.m.f and the time of roation for two periods or rotation.

omega

Identify which of the following function represent simple harmonic motion. <br> (i)

Y = Ae^(I omega t)

(ii)

Y = a e^(- omega t)

<br> (iii)

y = a sin^(2) omega t

(iv)

y = a sin omega t + b cos omega t

<br> (v)

y = sin omega t + b cos 2 omega t

Latest Blog Post

View All