Logika Matematika Practice Questions
UN (Indonesia) · UN Matematika · 147 free MCQs with instant results and detailed explanations.
147
Total
43
Easy
74
Medium
30
Hard
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Sample Questions from Logika Matematika
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Q1
Easy
If P represents 'It is raining' and Q represents 'The ground is wet', which of the following statements correctly represents 'If it is raining, then the ground is wet'?
A.
P → Q
B.
Q → P
C.
P ∧ Q
D.
P ∨ Q
Show Answer & Explanation
Correct Answer: A
The statement 'If it is raining, then the ground is wet' is a conditional statement, which is represented by 'P → Q'. This indicates that if P is true, then Q must also be true.
Q2
Easy
Which of the following is the contrapositive of the statement: 'If it is sunny, then we will go to the park'?
A.
If we do not go to the park, then it is not sunny.
B.
If it is not sunny, then we will not go to the park.
C.
If we go to the park, then it is sunny.
D.
If it is sunny, then we will not go to the park.
Show Answer & Explanation
Correct Answer: A
The contrapositive of a statement 'If P, then Q' is 'If not Q, then not P'. In this case, 'If we do not go to the park (not Q), then it is not sunny (not P)'.
Q3
Easy
In a logical argument, if the premises are true, what can be said about the conclusion in a valid argument?
A.
The conclusion must be true.
B.
The conclusion could be false.
C.
The conclusion is always false.
D.
The conclusion is irrelevant.
Show Answer & Explanation
Correct Answer: A
In a valid logical argument, if the premises are true, the conclusion must also be true. This is the fundamental principle of deductive reasoning.
Q4
Medium
If p is true and q is false, what is the truth value of the expression p AND q?
A.
True
B.
False
C.
Indeterminate
D.
Cannot be determined
Show Answer & Explanation
Correct Answer: B
The expression p AND q is true only if both p and q are true. Since q is false, the overall expression evaluates to false.
Q5
Medium
In a logical expression, how many distinct truth values can the expression (p OR NOT p) have?
A.
1
B.
2
C.
3
D.
4
Show Answer & Explanation
Correct Answer: A
The expression (p OR NOT p) is always true, regardless of the truth value of p. It represents a tautology.
Q6
Medium
Which of the following represents the negation of the statement: 'All birds can fly'?
A.
Some birds cannot fly.
B.
All birds cannot fly.
C.
No birds can fly.
D.
Some birds can fly.
Show Answer & Explanation
Correct Answer: A
The negation of 'All birds can fly' is that there exists at least one bird that cannot fly, which is represented by 'Some birds cannot fly.'
Q7
Medium
If the statement p is true, what can be concluded about the expression NOT (p AND q) when q is false?
A.
True
B.
False
C.
Indeterminate
D.
Always true
Show Answer & Explanation
Correct Answer: A
Given p is true and q is false, p AND q is false. Hence, NOT (p AND q) is true, as it negates the false expression.
Q8
Hard
If a statement is logically equivalent to its contrapositive, which of the following pairs of statements is a valid example of this principle?
A.
If it rains, then I will stay home; If I do not stay home, then it does not rain.
B.
If I study hard, I will pass; If I do not pass, then I did not study hard.
C.
If I wake up early, I will exercise; If I do not exercise, then I did not wake up early.
D.
If I eat healthy, I will be fit; If I am not fit, then I do not eat healthy.
Show Answer & Explanation
Correct Answer: A
The contrapositive of 'If it rains, then I will stay home' is 'If I do not stay home, then it does not rain', which maintains logical equivalence.
Q9
Hard
Consider the logical expressions: p: 'It is sunny', q: 'I will go to the park'. What is the truth value of the expression (p ∧ q) → r if p is true, q is false, and r is true?
A.
True
B.
False
C.
Undefined
D.
Not determinable
Show Answer & Explanation
Correct Answer: B
The expression (p ∧ q) evaluates to false because q is false. A false premise leads to the entire expression being false, as the implication does not hold.
Q10
Hard
If the statement 'If A, then B' is true, which of the following statements must also be true?
A.
If B, then A
B.
If not A, then not B
C.
If not B, then not A
D.
If A and B, then true
Show Answer & Explanation
Correct Answer: C
The contrapositive of the statement 'If A, then B' is 'If not B, then not A', which is logically equivalent and must also be true.
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Logika Matematika — UN (Indonesia) UN Matematika Practice Questions Online
This page contains 147 practice MCQs for the chapter Logika Matematika in UN (Indonesia) UN Matematika. The questions are organized by difficulty — 43 easy, 74 medium, 30 hard — so you can choose the right level for your preparation.
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