Practical # 05

Object 01:Draw the Venn diagrams of the following “Events when we toss a dice twice

(or) toss two dice once.

A. {Sum of two dice number less than 7}B. {1st dice showing a number less than 4}C. {Either one dice showing 3}D. {1st dice number less than 2nd dice number}

Solution:

S = { (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,2) , (2,3) , (2,4) , (2,5), (2,6) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) , (4,1) , (4,2) , (4,3) , (4,4), (4,5) , (4,6) , (5,1) , (5,2) , (5,3) , (5,4) , (5,6) , (5,6) , (6,1) , (6,2) , (6,3), (6,4) , (6,5) , (6,6) }

A = { (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (2,1) , (2,2) , (2,3) , (2,4) , (3,1) , (3,2), (3,3) , (4,1) , (4,2) , (5,1) }

B = { (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,2) , (2,3) , (2,4) , (2,5), (2,6) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) }

C = {(1,3) , (2,3) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) , (4,3) , (5,3) , (6,3) }

D = { (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,3) , (2,4) , (2,5) , (2,6) , (3,4) , (3,5) , (3,6) , (4,5) , (4,6) , (5,6) }

A∩B = { (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (2,1) , (2,2) , (2,3) , 2,4) , (3,1) , (3,2) , (3,3) }

A∩C = { (1,3) , (2,3) , (3,1) , (3,2) , (3,3) }

A∩D = { (1,2) , (1,3) , (1,4) , (1,5) , (2,3) , (2,4) }

B∩C = { (1,3) , (2,3) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) }

B∩D = { (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,3) , (2,4) , (2,5) , (2,6) , (3,4) , (3,5) , (3,6) }

D∩C = { (1,3) , (2,3) , (3,4) , (3,5) , (3,6) }

A∩B∩C = { (1,3) , (2,3) , (3,1) , (3,2) , (3,3) }

A∩B∩D = { ((1,2) , (1,3) , (1,4) , (1,5) , (2,3) , 2,4) }

A∩C∩D = { (1,3) , (2,3) }

B∩C∩D = { (1,3) , (2,3) , (3,4) , (3,5) , (3,6) }

A∩B∩C∩D = { (1,3) , (2,3) }

V ENN D IAGRAM :