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WorksheetsQuiz 1 - (Prelim - Discrete Mathematics)
Total questions: 50
Worksheet time: 26mins
Proof involving indirect reasoning. Also called proof by contradiction
Direct reasoning
Indirect reasoning
Direct proof
Indirect Proof
The second step of an indirect proof is to ____?
assume the negation of the given
assume the negation of what you are trying to prove
conclude the prove is true
contradict the given using logical statements based on the initial assumption
there can be only one 90 angle in a triangle
A way to reach a conclusion using reasoning:
Proof
hypothesis
counterexample
A proof that can be used when there are only two possibilities; if one possibility is false, the other must be true.
direct proof
indirect proof
conclusion
An example that shows a statement is false:
hypothesis
conclusion
counterexample
"Grass is green."
Proposition
Not Proposition
"Close the door."
Proposition
Not proposition
"x is greater than 2"
Proposition
Not proposition
"Fish can fly."
Proposition
Not proposition
"A snail can sleep for three years."
Proposition
Not proposition
"A rhinoceros' horn is made of hair."
Proposition
Not proposition
What is a proposition?
An invariable word used to establish a dependency relationship between two or more words.
It is a statement with complete meaning and constitutes the most elementary form of logic.
It is a resinous mixture obtained by bees from tree buds.
None of the above.
Is a proposition and a statement the same thing?
Yes
Not
5. Negative/positive. They are those propositions that:
Express a state of affairs (the positive ones) or the very absence of that state (the negative ones).
Express a state of affairs (the negative ones) or the very absence of that state (the positive ones).
An example of a simple proposition is:
Cat
Her cat is brown
Is brown
Her cat
Compound propositions appear mediated by the presence of some kind of connector, which can be opposition (or), addition (and), or condition (if). In addition, negative propositions, which include the word no, are considered compounds.
True
False
This symbol, ∧, means?
and
or
not
if, then
This symbol, ∨, means?
and
or
not
if, then
What type of logic is this table showing:
AND
OR
IF, THEN
Which of the following is NOT an acceptable set of possible True and False Combinations
Which of the following set of values would correctly complete this table?
T F F F
T T F F
T T T F
F T F T
Which of the following combinations of truth values would be correct for this truth table?
T F T F
T T T F
F T F T
T F F T
Which of the following sets of truth values would correctly complete this truth table?
F F F T
F T T F
T F T T
F T F T
Which set of truth values would correctly complete this table?
T F T F
F T T T
F F T T
F F F T
What type of logic is this table showing:
AND
OR
NOT
XOR
Use the logic condition to find the value of X:
A and not B
True
False
Use the logic condition to find the value of X:
Not A or B
True
False
Use the logic condition to find the value of Y:
A or B or C
True
False
Use the logic condition to find the value of X:
A or (B and C)
True
False
Use the logic condition to find the value of W:
not A or B or C
True
False
Which of the following statement is a proposition?
Get me a glass of milkshake
God bless you!
What is the time now?
The only odd prime number is 2
Which of the following option is true?
If the Sun is a planet, elephants will fly
3 +2 = 8 if 5-2 = 7
1 > 3 and 3 is a positive integer
-2 > 3 or 3 is a negative integer
Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is?
If I love cricket then I am in Bangalore
If I am in Bangalore then I love cricket
I am not in Bangalore
I love cricket
Let P: I am in Delhi.; Q: Delhi is clean.; then q ^ p(q and p) is?
Delhi is clean and I am in Delhi
Delhi is not clean or I am in Delhi
I am in Delhi and Delhi is not clean
Delhi is clean but I am in Mumbai
p → q is logically equivalent to
∼q → p
∼p → q
∼ p ∧ q
∼p ∨ q
Which of the following is a well-defined set?
A set of beautiful teachers
A set of basketball players
A set of President of the Republic of the Philippines
A set of Class Honors
List all the letters in the name " jennylyn"
{j,e,n,n,y,l,y,n}
{j,e,n,y,l,y,n}
{j,e,n,y,l}
{j.e.n}
Given the set of letters in the word "mathematics", what is the cardinality of the given set?
11
8
6
4
reasoning is a type of reasoning that reaches conclusions based on a pattern.
Inductive
Conjecture
is a statement that is based on inductive reasoning but has not yet been shown to be true.
Inductive
Conjecture
Which is a valid conclusion for....
If I run in the morning then I feel energized
If I am energized then I have a great day
If I am energized then I have a great day
I have a great day
I am energized
If I run in the morning then I have a great day
Let p represent "x is an even number" and q represent "x is divisible by 4" Which of the following is true when x = 10?
p∧qp∨q
∼p
q
What is the converse of the statement "If it is Sunday, then I don't go to school"?
If it is not Sunday, then I do not go to school.
If I go to school, then it is not Sunday
If I do not go to school, then it is Sunday.
If it is not Sunday, then I go to school
What is the contrapositive of the statement "If I study, then I pass the test"?
I pass if I study
If I pass the test, then I study
If I do not study, then I do not pass
If I do not pass the test, then I did not study
