If `L = {1,2,3,4}, M = {3,4,5,6}` and `N = {1,3,5}`, then verify that `L - (M uu N) = (L-M) nn (L-N)`.

If L= {1, 2, 3, 4}, M= {3, 4, 5, 6} and N= {1, 3, 5}, then verify that L - (M cup N)= (L - M) cap (L - N) .

Given L={1,2,3,4}, M={3,4,5,6} and N={1,3,5} Verify that L-(McupN)=(L-M)cap(L-N) .

Given L, = {1,2, 3,4},M= {3,4, 5, 6} and N= {1,3,5} Find L-(M⋃N).

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has//have the same energy lists: 1. n = 4, l = 2, m_l = -2 , m_s = - 1//2 2. n = 3, l = 2, m_l = 1, m_s = +1//2 3. n = 4, l = 1, m_l = 0, m_s = + 1//2 4. n = 3, l = 2, m_l = -2 , m_s = -1//2 5. n = 4, l = 1, m_l = 0 , m_s = +1//2

Explain giving reasons which of the following sets of quantum number are not possible (a ) n=0, l =0 m_(l) = 0, m_(s ) =+ (1)/(2) ( b) n=1 , l = 0 m_(l) = 0, m_(s ) = - (1)/(2) ( c) n=1 , l = 1, m_(l ) = 0, m_(s ) = + (1)/(2) (d ) n= 2, l = 1, m_(l ) = 0, m_(s ) = (1) /(2) ( e) n=3, l = 3, m_(l) = 3, m_(s ) = + (1)/(2) (f ) n=3, l = 1, m_(l) = 0, m_(s) l = + (1)/(2)

Describe the orbital with the following quantum numbers : (i) n = 1, l = 0 " " (ii) n = 2, l = 1, m = 0 (iii) n = 3, l = 2 " " (iv) n = 4, l = 1 (v) n = 3, l = 0, m = 0 " " (vi) n = 3, l = 1 .

The quantum numbers of six elements are given below. Arrange them in order of increasing energies. If any of these combinations has/have the same energies, list them. {:((1) n = 4 ",", l = 2",", m_l=-2",", m_s = - 1/2),((2) n = 3 ",", l = 2",", m_l=0",", m_s = + 1/2),((3) n = 4 ",", l = 1",", m_l= 0",", m_s = + 1/2),((4) n = 3 ",", l = 2",", m_l=-2",", m_s = - 1/2),((5) n = 3 ",", l = 1",", m_l=-1",", m_s = + 1/2),((6) n = 4 ",", l = 1",", m_l=0",", m_s = + 1/2):}

ABCD is a square of lengths a, a in N, a gt 1 . Let L_(1),L_(2),L_(3) ... Be points BC such that BL_(1) = L_(1)L_(2) = L_(2)L_(3) = ....=1 and M_(1), M_(2), M_(3)... be points on CD such that CM_(1) = M_(1)M_(2) = M_(2)M_(3) = ...=1 .Then, sum_(n= 1)^(a-1)(AL_(n)^(2) + L_(n)M_(n)^(2)) is equal to