Discrete math
write statement with symbolic forms ٨،٧،~ Q# 6, 7
Q#6 : Let s =” stock are increasing” and i= “interested rates are steady” .
a. stuck are increasing but interested rates are steady.
b. Neither are stocks increasing nor are interested rates steady.
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Q#7: Jun is a math major but not a computer science major.
(m= “jun is maat major ” , c=” jun is a computer science major”.
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#Use the truth table for statement form.
Q#13: ~(p ٨ q ) v (p v q).
# determine whether the statement forms are logically equivalent. In the case construct a truth table and include a sentence to justify your answer that should show ur understanding to logical equivalent.
Q#17: ~( p ٨ q)and ~p ٨ ~q.
Q#22: p ^ (q V r )and ( p ^ q) V ( p ^r )
#Use the truth table to establish which statement form are tautologies and which are contradictions .
Q#42 : ((~p ^ q )^ (q ^ r )) ^ ~q
Q#43 :(~ p V q ) V ( p ^ ~q)
Q#49 : (pV ~ q ) ^ ( ~p V ~q ) logically equivalent to :
a. (~q V p ) ^ (~q V ~p)
b. ~q V ( p ^ ~ p )
c. ~q V c
d. ~q
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Section 2.2
# rewrite the statement in If, then form :
Q#4 : Fix my ceiling or I won’t pay my rent.
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construct a truth table for the statement form:
Q# 10 ( p→ r ) ↔(q →r)
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Q# 15 : Determine whether the following statement are logically equivalent.
p →( q →r) and ( p→ q ) →r.
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Q#24:use truth table to establish truth of each statement
24. A conditional statement is not logically equivalent to its converse.
27. the converse and inverse of conditional statement are logically equivalent to each other.
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if statement forms p and Q are logically equivalent, then p ↔q is tautology. conversely p ↔ q is also logically equivalent . use ↔ to convert the logical equivalencies to tautology. then use a truth table to verity.
Q#31:p → ( q →r ) = ( p ^ q )→r
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rewrite statement in If, then form:
Q#41:having two 45 angles is sufficient condition for the triangle to be right triangle
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use contrapositive to rewrite the statement in if, then form in two ways.
Q# 43: Doing HW regularly is necessary condition for Jim to pass the course.
