MA110 Tutorial Sheet 2025 PDF

TIItr COPPIRI]I'LT UNIVEIISITY SCTIOOL OF NIA'I'HI.]MA'I'ICS AND NATURAL SCTENCIIS DEPAITI'MI'N'T OT MATIII'MATICS l'U'l OIttAL SI lliill I : MAI I0 - Nlathcnrarical lVlcthods...

TIItr COPPIRI]I'LT UNIVEIISITY SCTIOOL OF NIA'I'HI.]MA'I'ICS AND NATURAL SCTENCIIS DEPAITI'MI'N'T OT MATIII'MATICS l'U'l OIttAL SI lliill I : MAI I0 - Nlathcnrarical lVlcthods 2025 l. i) Prove the Dc Morgan's Larvs: a) (B n C), B, U C, = b) (B u c)' = B' n c' ii) I)rovc that (A,), = A )-. Il' C c D, thcn sinrplily il'possiblc i) cnD ii)c,uD, iii)cuD, iv) c,n(cuD) 3. ll'C atul D are riisjoint. sinrplily ilpossihlc i) c' o D, ii) c, u D, iii) (c n D), iv) (c a D), 'l tJsing the associative and distrihutivc propcrtics oIunion ancl intersection olsets.Show rhat Iiii) tAu(A'^B)=AuB - f!."8).u(A^8,) ii) Au B: (An B)u(An B,)u (A,^B) 5. a ) Ciivcn that X. y and 7. arc scts, sinrplily the following ilpossible nlx'u (y nz)l' ii\y,n(x uy) iii) (x n v;L6 ny,) iv)(x uv) o(x try,) b) (iivcn that ,\ and l' :rrc subscts ol'so,rc universal set U, sinrplily the lollor.ving: (i) -r (-1a' al I). (ii) ^ [(,L.\ ]'),. (_\', u ].)j,. 6,.a) I-etA={x €R: -4