ONE-EIGHTH STAGE 2025
Ghana National College: 65 points
Tema Secondary School: 33 points
Effiduase SHCS: 28 points
Mankranso SHS: 43 points
St Paul's SHS, Denu: 23 points
Adonten SHS: 14 points
St. Thomas Aquinas SHS: 51 points
Tamale SHS: 37 points
O'Reilly SHS: 25 points
ROUND 4 - TRUE OR FALSE
SET ONE
1. Division is closed on the set of integers.
ANSWER: FALSE
EXPLANATION:
Closure means that dividing any two integers should always give another integer.
But $5 \div 2=2.5$. 2.5 is not an integer.
Therefore division is not closed on the set of integers.
2. Division is closed on the set of non-zero rational numbers.
ANSWER: TRUE
EXPLANATION:
Closure means that dividing any two non-zero rational numbers should always give another non-zero rational number.
Which is always true.
3. Division is closed on the set of irrational numbers.
ANSWER: FALSE
EXPLANATION:
This statement is false since $\frac{\sqrt{2}}{\sqrt{2}}=1$, which is a rational number.
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PRACTICE QUESTIONS
1. QUESTION: Addition is closed on the set of integers.
ANSWER: TRUE
EXPLANATION:
The sum of two integers is an integer.
2. QUESTION: Subtraction is closed on the set of natural numbers.
ANSWER: FALSE
EXPLANATION:
$3 - 5 = -2$, which is not a natural number.
3. QUESTION: Multiplication is closed on the set of integers.
ANSWER: TRUE
EXPLANATION:
The product of two integers is an integer.
4. QUESTION: Addition is closed on the set of irrational numbers.
ANSWER: FALSE
EXPLANATION:
$\sqrt{2} + (-\sqrt{2}) = 0$, which is rational.
5. QUESTION: Multiplication is closed on the set of rational numbers.
ANSWER: TRUE
EXPLANATION:
$\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}$, which is rational.
6. QUESTION: Subtraction is closed on the set of integers.
ANSWER: TRUE
EXPLANATION:
The difference of two integers is an integer.
7. QUESTION: Multiplication is closed on the set of odd integers.
ANSWER: TRUE
EXPLANATION:
The product of two odd integers is odd.
8. QUESTION: Addition is closed on the set of odd integers.
ANSWER: FALSE
EXPLANATION:
$3 + 5 = 8$, which is even.
9. QUESTION: Addition is closed on the set of even integers.
ANSWER: TRUE
EXPLANATION:
The sum of two even integers is even.