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Answer TRUE or FALSE for each of (a)-(e). No justification is required for this problem. a) If A is the adjacency matrix of a tree on n vertices, then the sum of entries of A is 2. (n-1). o) For finite sets A and B, AUB|+|AnB| = |A|+|B|. c) If ao = 1 and the sequence an is given by an = 8. an-1 for all n ≥ 1, then the explicit formula is given by an 8" for all n ≥ 1.

Answer TRUE or FALSE for each of (a)-(e). No justification is required for this problem. a) If A is the adjacency matrix of a tree on n vertices, then the sum of entries of A is 2. (n-1). o) For finite sets A and B, AUB|+|AnB| = |A|+|B|. c) If ao = 1 and the sequence an is given by an = 8. an-1 for all n ≥ 1, then the explicit formula is given by an 8" for all n ≥ 1.

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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### Question 1: Answer TRUE or FALSE for each of (a)-(e). No justification is required for this problem. #### (a) If \( A \) is the adjacency matrix of a tree on \( n \) vertices, then the sum of entries of \( A \) is \( 2 \cdot (n - 1) \). #### (b) For finite sets \( A \) and \( B \), \( |A \cup B| + |A \cap B| = |A| + |B| \). #### (c) If \( a_0 = 1 \) and the sequence \( a_n \) is given by \( a_n = 8 \cdot a_{n-1} \) for all \( n \geq 1 \), then the explicit formula is given by \( a_n = 8^n \) for all \( n \geq 1 \). #### (d) The total degree of the graph \( K_{1,3} \) is even. #### (e) If \( b_n = 2 \cdot b_{n-1} + 8 \) for all \( n \geq 1 \), and \( b_0 = -9 \), then \( b_3 = -10 \).
Transcribed Image Text:### Question 1: Answer TRUE or FALSE for each of (a)-(e). No justification is required for this problem. #### (a) If \( A \) is the adjacency matrix of a tree on \( n \) vertices, then the sum of entries of \( A \) is \( 2 \cdot (n - 1) \). #### (b) For finite sets \( A \) and \( B \), \( |A \cup B| + |A \cap B| = |A| + |B| \). #### (c) If \( a_0 = 1 \) and the sequence \( a_n \) is given by \( a_n = 8 \cdot a_{n-1} \) for all \( n \geq 1 \), then the explicit formula is given by \( a_n = 8^n \) for all \( n \geq 1 \). #### (d) The total degree of the graph \( K_{1,3} \) is even. #### (e) If \( b_n = 2 \cdot b_{n-1} + 8 \) for all \( n \geq 1 \), and \( b_0 = -9 \), then \( b_3 = -10 \).
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Can part d and e be answered as well. They are also true or false

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