Question

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

Answer 1

S = true
~s = false
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j = false
~j = true
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~s = false and j = false, so,
~s v j = (false) v (false)
~s v j = false
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Similarly,
s v ~j = (true) v (true)
s v ~j = true
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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
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The final answer is false