Question

answer ASAP

(I ) Given the following assumptions : P is True, Q is False, R is True

Determine the final answer for the following propositions

1) P --> Q --> ~R

2) ( ~ P <---> ~ R ) V P

3) (P V Q V ) <---> R

(II) Given the following sets

A = { 1, 3, 5, 7, 9, 19, 29 }, B = { 1, 5, 3}, C = {7, 8, 14}, D = {7,8, 22, 88}

1) what is B U C

2) is B a subset of A

3) is C a proper subset of A

4) what is the intersect of C and D sets

5) Assume that A is a a universal set

( III)   a) draw the venn diagram to represent the relationship between A and B

b) draw the venn diagram to represent the relationship between C and D

Answer 1

Solution (I):-

P is True, Q is False, R is True

1) P --> Q --> ~R
True -> False -> ~True
False -> ~True
False -> False
True
So the final answer would be True.

2) ( ~ P <---> ~ R ) V P
( ~ True <---> ~ True) V True
(False <---> False) V True
True V True
True
So the final answer would be True.

3) (P V Q V ) <---> R
(True V False) <---> True
True <---> True
True
So the final answer would be True.

Solution (II):-

A = { 1, 3, 5, 7, 9, 19, 29 }, B = {1, 5, 3}, C = {7, 8, 14}, D = {7,8, 22, 88}

1) B U C = {1,5,3,7,8,14}

2) B is a subset of A because all the elements of B are present in the set A that are {1,5,3}.

3) C is not a proper subset of A as the elements of C = {7, 8, 14} are not present in the set A so it is not subset also.

4) The intersect of C and D sets constitutes the set containing elements {7,8}. So set C intersect D = {7,8}.

5) A cannot be the universal set because it doesn't contain all the given sets B , C , D in it .

Solution (III):-

(a) venn diagram to represent the relationship between A and B as B is the subset of A.

(b) venn diagram to represent the relationship between C and D as there exists C intersect D set ={7,8}.