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Consider the following sets. The universal set for this problem is the set of all quadrilaterals. A The set of all parallelograms. B = The set of all rhombuses. C = The set of all rectangles. D = The set of all trapezoids. Using only the symbols x, A, B, C, D, E, ≤, =, ‡, n, u, x,', Ø, (, and ), and write the following statements in set notation. (a) The polygon x is a parallelogram, but it isn't a rhombus. O xEA and xe B OXEAU B' OXE (AUB)' OXE (ANB)' OXEAN B' (b) There are other quadrilaterals besides parallelograms and trapezoids. O (AND)' = 0 O AUDE BUC O (AUD)' # Ø O ANDEBUC OA'N D'=Ø (c) Both rectangles and rhombuses are types of parallelograms. O CUBEA and A ≤ CUB O (CUB)' ≤ A O CUBSA OCNBEA

Consider the following sets. The universal set for this problem is the set of all quadrilaterals. A The set of all parallelograms. B = The set of all rhombuses. C = The set of all rectangles. D = The set of all trapezoids. Using only the symbols x, A, B, C, D, E, ≤, =, ‡, n, u, x,', Ø, (, and ), and write the following statements in set notation. (a) The polygon x is a parallelogram, but it isn't a rhombus. O xEA and xe B OXEAU B' OXE (AUB)' OXE (ANB)' OXEAN B' (b) There are other quadrilaterals besides parallelograms and trapezoids. O (AND)' = 0 O AUDE BUC O (AUD)' # Ø O ANDEBUC OA'N D'=Ø (c) Both rectangles and rhombuses are types of parallelograms. O CUBEA and A ≤ CUB O (CUB)' ≤ A O CUBSA OCNBEA

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following sets. The universal set for this problem is the set of all quadrilaterals. - \( A \) = The set of all parallelograms. - \( B \) = The set of all rhombuses. - \( C \) = The set of all rectangles. - \( D \) = The set of all trapezoids. Using only the symbols \( x, A, B, C, D, \in, \notin, \subseteq, =, \neq, \cap, \cup, \times, ', \varnothing, (, \) \), write the following statements in set notation. (a) The polygon \( x \) is a parallelogram, but it isn’t a rhombus. - \( \circ \, x \in A \text{ and } x \notin B \) - \( \circ \, x \in A \cup B' \) - \( \circ \, x \in (A \cap B)' \) - \( \circ \, x \in A \cap B' \) (b) There are other quadrilaterals besides parallelograms and trapezoids. - \( \circ \, (A \cap D)' \neq \varnothing \) - \( \circ \, A \cup D \subset B \cup C \) - \( \circ \, (A \cup D)' \neq \varnothing \) - \( \circ \, A \cap D \subset B \cup C \) - \( \circ \, A' \cap D' = \varnothing \) (c) Both rectangles and rhombuses are types of parallelograms. - \( \circ \, C \cup B \subset A \text{ and } A \subset C \cup B \) - \( \circ \, (C \cup B)' \subset A \) - \( \circ \, C \cup B = A \) - \( \circ \, C \cap B \subset A \) - \( \circ \, C \cap B \subset A \text{ and } A \subset C \cap B \)
Transcribed Image Text:Consider the following sets. The universal set for this problem is the set of all quadrilaterals. - \( A \) = The set of all parallelograms. - \( B \) = The set of all rhombuses. - \( C \) = The set of all rectangles. - \( D \) = The set of all trapezoids. Using only the symbols \( x, A, B, C, D, \in, \notin, \subseteq, =, \neq, \cap, \cup, \times, ', \varnothing, (, \) \), write the following statements in set notation. (a) The polygon \( x \) is a parallelogram, but it isn’t a rhombus. - \( \circ \, x \in A \text{ and } x \notin B \) - \( \circ \, x \in A \cup B' \) - \( \circ \, x \in (A \cap B)' \) - \( \circ \, x \in A \cap B' \) (b) There are other quadrilaterals besides parallelograms and trapezoids. - \( \circ \, (A \cap D)' \neq \varnothing \) - \( \circ \, A \cup D \subset B \cup C \) - \( \circ \, (A \cup D)' \neq \varnothing \) - \( \circ \, A \cap D \subset B \cup C \) - \( \circ \, A' \cap D' = \varnothing \) (c) Both rectangles and rhombuses are types of parallelograms. - \( \circ \, C \cup B \subset A \text{ and } A \subset C \cup B \) - \( \circ \, (C \cup B)' \subset A \) - \( \circ \, C \cup B = A \) - \( \circ \, C \cap B \subset A \) - \( \circ \, C \cap B \subset A \text{ and } A \subset C \cap B \)
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