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solve the recurrence relation using generating functions An+1-An=3n )n>0 with AQ=1
Translate the statement into propositional logic using the propositions provided.
You cannot edit a protected Wikipedia entry unless you are an administrator. Express your answer in terms of e: “You can edit a protected Wikipedia entry” and a: “You are an administrator.”
Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives.
a) No one is perfect.
b) Not everyone is perfect.
c) All your friends are perfect.
d) At least one of your friends is perfect.
e) Everyone is your friend and is perfect.
f) Not everybody is your friend or someone is not perfect.
Show that (p ∧ q) → (p ∨ q) is a tautology.
Which of these are propositions? What are the truth values of those that are propositions? Write P and its truth value either True or False if Proposition and NP if not a proposition and write what made it not a proposition.
a) Do not pass go.
b) What time is it?
c) 4 + x = 5.
d) The moon is made of green cheese.
e) 2n≥ 100.
f) 1+2=5
Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives.
a) No one is perfect.
b) Not everyone is perfect.
c) All your friends are perfect.
d) At least one of your friends is perfect.
e) Everyone is your friend and is perfect.
f) Not everybody is your friend or someone is not perfect. Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives.
a) No one is perfect.
b) Not everyone is perfect.
c) All your friends are perfect.
d) At least one of your friends is perfect.
e) Everyone is your friend and is perfect.
f) Not everybody is your friend or someone is not perfect.
The number of transitive closure exists in the relation R = {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} where {1, 2, 3, 4, 5} ∈ A is__________.
Suppose a, b, c, d have proper positions 1, 2, 3, 4 respectively, i.e., the correct sequence (from position 1 to 4) is a, b, c, d. Write down all the deranged sequences. What is the combinatorial expression for their count?
[￢p ∧(p ∨ q)]→q
For each of the ff. sets, determine whether 2 is an element of that set.
a. {𝑥∈ℝ|𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 1}
b. {𝑥∈ℝ|𝑥 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 𝑜𝑓 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟}
c. {2,{2}}
d. {{2},{{2}}}
