Answer: The proofs are given below.
Step-by-step explanation: We are given to prove that the following statements are tautologies using truth table :
(a) ¬r ∨ (¬r → p) b. ¬(p → q) → ¬q
We know that a statement is a TAUTOLOGY is its value is always TRUE.
(a) The truth table is as follows :
r p ¬r ¬r→p ¬r ∨ (¬r → p)
T T F T T
T F F T T
F T T T T
F F T F T
So, the statement (a) is a tautology.
(b) The truth table is as follows :
p q ¬q p→q ¬(p→q) ¬(p→q)→q
T T F T F T
T F T F T T
F T F T F T
F F T T F T
So, the statement (B) is a tautology.
Hence proved.
Statement 3 and 4 are true as Figures 1 and 2 are not congruent and Figures 1 and 3 are not congruent
<h3>What are Congruent Figures ?</h3>
The figures that are similar in shape and size or can be mapped into one another , such figures are called Congruent Figures.
The graph has been plotted on the basis of given data.
The plot can be seen in the graph attached with the answer.
The statements that are true according to the given data is
Statement 3 and 4 are true as
Figures 1 and 2 are not congruent because figure 1 cannot be mapped onto figure 2 using a sequence of rigid transformations.
Figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a sequence of rigid transformations.
To know more about Congruent Figures
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Answer:
The graph of given function is shown below.
Step-by-step explanation:
The absolute parent function is g(x)=|x|. The graph of parent function is a V-shape d and vertex of the function is origin.
The given function is
.... (1)
The vertex from of an absolute function is
.... (2)
where, a is a constant and (h,k) is vertex of the function.
From (1) and (2) we get

The value of a is -1. The value of a is negative it means the graph of parent function reflect across x-axis.
The vertex of the function is (0,-2). It means the graph of parent function shifts 2 units down.
The graph of given function is shown below.
Answer:
i think its B or C most likely C
Step-by-step explanation:
Answer:
21, 24, 29
Step-by-step explanation:
Replace n with 1, 2, and 3, and do the arithmetic.
first term = 1² +20 = 21
second term = 2² +20 = 24
third term = 3² +20 = 29
The first three terms are 21, 24, 29.