If s is true and j is false, is the following true or false (~s v j) ^ (s v~ j)

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zynerrius32645ox5njq zynerrius32645ox5njq

01-10-2017
Mathematics

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If s is true and j is false, is the following true or false (~s v j) ^ (s v~ j)

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jimthompson5910 jimthompson5910 · Answer 1 · 2017-10-01T20:06:36+02:00

s = true
~s = false
-------------
j = false
~j = true
-------------
~s = false and j = false, so,
~s v j = (false) v (false)
~s v j = false
-------------
Similarly,
s v ~j = (true) v (true)
s v ~j = true
-------------
We have
~s v j = false
and
s v ~j = true
which lead to this when we conjunct the two logical expressions
(~s v j) ^ (s v ~j) = (false) ^ (true)
(~s v j) ^ (s v ~j) = false
-------------
-------------
The final answer is false