Interactive multiple-choice quiz: Logic and Geometry Assessment
This document covers compound statements, truth values, and geometric symmetry. Students will analyze statements with conjunctions, disjunctions, and negations. The quiz also includes exercises on identifying lines of symmetry in polygons.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Use the statements based on the provided figure to find the truth value for: p and r p: The figure is a trapezoid. q: The figure has four congruent sides. r: The figure has four right angles.
Explanation
The figure is a square, which is not a trapezoid, so statement p is false. A conjunction (and) is only true if both parts are true.
Question 2
Points: 1
Use the statements based on the provided figure to find the truth value for: $\sim p \wedge q$ p: The figure is a trapezoid. q: The figure has four congruent sides. r: The figure has four right angles.
Explanation
The figure is not a trapezoid, so $\sim p$ (not p) is true. It has four congruent sides, so q is true. Both parts are true, so the conjunction is true.
Question 3
Points: 1
Use the statements to find the truth value for: $q \vee \sim r$ p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2 + 8 > 10
Explanation
q is true because vertical angles are always congruent. In a disjunction (or), if at least one part is true, the entire statement is true.
Question 4
Points: 1
Use the statements to find the truth value for: $r \vee q$ p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2 + 8 > 10
Explanation
Even though r is false (10 is not greater than 10), q is true. One true part makes the disjunction true.
Question 5
Points: 1
Use the statements to find the truth value for: $\sim r \vee \sim p$ p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2 + 8 > 10
Explanation
r is false, so $\sim r$ is true. Since the first part of the disjunction is true, the entire statement is true.
Question 6
Points: 1
Use the statements to find the truth value for: p and q p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2 + 8 > 10
Explanation
p is true (-3 - 2 = -5) and q is true. Since both parts of the conjunction are true, the statement is true.
Question 7
Points: 1
Use the statements to find the truth value for: $p \wedge r$ p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2 + 8 > 10
Explanation
p is true, but r is false because 2 + 8 = 10. A conjunction requires both parts to be true.
Question 8
Points: 1
Use the statements to find the truth value for: $\sim p \wedge \sim q$ p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2 + 8 > 10
Explanation
p is true and q is true, making their negations false. A conjunction with false components is false.
Question 9
Points: 1
Determine whether the figure has a line of symmetry. If so, state how many lines of symmetry it has.
Explanation
The figure is an equilateral triangle, which has 3 lines of symmetry passing through each vertex to the midpoint of the opposite side.
Question 10
Points: 1
Determine whether the figure has a line of symmetry. If so, state how many lines of symmetry it has.
Explanation
The figure is a regular hexagon, which has 6 lines of symmetry (3 passing through opposite vertices and 3 through midpoints of opposite sides).
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