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Show, by the use of replacement rules, that (-p ^ q) ^ (q→p) = F
are logically equivalent.
- Show, by the use of the truth table/matrix, that the statement is a tautology.
Show, by the use of the truth table (truth matrix), that the is a contradiction.
( pvq ) へ [ ( -p ) へ ( -q ) ]
Show that -p > (q → r) and q → (p V r) are logically equivalent.
Symbolize the following by using qualifiers, predicates and logical connectives.
- All rational numbers are real numbers.
- some rational numbers are integers.
- some even numbers are multiplied of two four and five.
- some triangles are scalene.
- every integer is multiple of 10 if and only if it is a mulple of 5 and 2.
Let R be the relation on the set A = {a, b, c, d, e, f} and
R = {(a,a), (a,c ), (b,a ), (b b), (c,b), (c,c), (d,d), (d,c)}
Obtain transitive closure of R using Warshall’s algorithm.
D. Write in the form " if p then q", then write converse, inverse and contra positive of each of the following implications.
- it is necessary to do your homework to get a passing grade.
- if you read your lesson everyday, you will pass all your courses.
Express each of these propositions as an English sentence:
- -p
- p v q
- p ^ q
- p arrow left p
- p arrow right and left q
C. Let p and q be propositions
p: 4 is a rational number
q: √3 is an irrational number
write the negation of these propositions
- Today is Monday
- The air in Naic Cavite is hot and polluted.
- Summer in Davao is hot and sunny.
- 2 + 1 > 5
- it is hot.
- X + y = 4
- 7. sierra madre mountains are denuded.
- a x b > 6
- it's raining in August.
- it is cold in December
