Question

Let the universal set U={0,1,2,3,4,5,6,7,8,9} and three subsets of it defined as: P={1,2,3,4} Q={4,5,6} R={3,4,6,8,9} Adapt the following propositional formulas: p / (q / r) = (p / q) / (p / r) p / (q / r) = (p / q) / (p / r) ~(p / q) = ~p / ~q ~(p / q) = ~p / ~q (p=>q) = (~q => ~p) (p => q) / (q => r) => (p => r) to their equivalents in the Boolean Algebra of the subsets of U. a) replace each propositional variable with its upper case equivalent (p->P, q->Q, r->R) b) replace each of the logic connectives with their corresponding equivalent in the Boolean Algebra of the subsets of the universal set U. Note that you will need to use the fact that p=>q is equivalent to ~p / q and that ~p will correspond to the complement of a subset of the universal set U. 1) For each of the resulting statements about sets, verify that they are true, by computing the results on the left and right side of the "=" symbols, or when "=" is absent, show that the result is the universal set U.

Name: let the universal set u0123456789 and three subsets of it defined as p1234 q456 r34689 adapt the following propositional formulas p q r p q p r p q r p q p r p q p q p q p q pq q p p q q r p 47169
Uploaded: 2023-07-23T09:04:05-08:00
Duration: 15 s
Channel: Numerade
Description: let the universal set u0123456789 and three subsets of it defined as p1234 q456 r34689 adapt the following propositional formulas p q r p q p r p q r p q p r p q p q p q p q pq q p p q q r p 47169

          Let the universal set U={0,1,2,3,4,5,6,7,8,9} and three  subsets of it defined as:
P={1,2,3,4}
Q={4,5,6}
R={3,4,6,8,9}
Adapt the following propositional formulas:
p / (q / r) = (p / q) / (p / r) 
p / (q / r) = (p / q) / (p / r)
~(p / q) = ~p / ~q 
~(p / q) = ~p / ~q
(p=>q) = (~q => ~p)
(p => q) / (q => r)  =>  (p => r) 
to their equivalents in the Boolean Algebra of the subsets of U.
a) replace each propositional variable with its upper case equivalent (p->P, q->Q, r->R)
b) replace each of the logic connectives with their corresponding equivalent in the Boolean Algebra of the subsets of the universal set U. Note that you will need to use the fact that p=>q is equivalent to ~p / q and that ~p will correspond to the complement of a subset of the universal set U.
1) For each of the resulting statements about sets, verify that they are true, by computing the results on the left and right side of the "=" symbols, or when "=" is absent, show that the result is the universal set U.

let the universal set u0123456789 and three subsets of it defined as p1234 q456 r34689 adapt the following propositional formulas p q r p q p r p q r p q p r p q p q p q p q pq q p p q q r p 47169

Added by Jose Antonio T.

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