In June 2024
Search & Filtering
1. \\((p\\wedge q)= (q\\wedge p)\\) and \\((p\\vee q) = (q\\vee p)\\) implies an _____ a. Idempotent Laws b. Associative laws c. Distributive Laws d. Commutative Laws 2. given that\\(A=\\begin{pmatrix}1 & 2 & 3\\\\ 4 & 5 & 6 \\end{pmatrix}\\)\nand \\[B=\\begin{pmatrix} 1 & 2\\\\ 3& 4\\\\ 5& 6 \\end{pmatrix}\\]\n. Find AB a. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 19 & 26 & 31\\\\ 29 & 40 & 51 \\end{pmatrix}\\) b. \\(\\begin{pmatrix} 5 & 12 & 15\\\\ 19 & 26 & 31\\\\ 29 & 40 & 51 \\end{pmatrix}\\) c. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 19 & 26 & 31\\\\ 20 & 40 & 45 \\end{pmatrix}\\) d. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 7 & 10 & 31\\\\ 20 & 40 & 45 \\end{pmatrix}\\)
a. \\(\\sim (\\sim p\\wedge \\sim q)\\)
b. \\((\\sim \\sim q)\\)
c. \\((p\\leftrightarrow q)\\)
d. \\((\\sim p\\wedge q)\\)
2. \\((p\\vee q)\\vee r=p\\vee (q\\vee r)\\) and \\((p\\wedge q)\\wedge r = p\\wedge (q\\wedge r)\\) implies an ___
a. Distributive Laws
b. Commutative Laws
c. Associative laws
d. Idempotent Laws
(█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5))
Q. Choose the correct answer.
Q. Let b and c are elements in a group G and e is identity element of G. If b5=c3=e,then inverse of bcb2 is
a. b2cb
b. b3c2b4
d. b2c2b4
1. N(x) = 0 if x=0.
2 N(xy) = N(x)N(y)
3. N(x) =1 if x is a unit
4. N(x) is prime if x is irreducible.
Is the statement true or false? Justify your answer.
Prove that N:Z[√d]→N∪{0}:N(a+b√d)=|a²-db²| satisfies the following properties for x,y∈Z[√d] :
i) N(x) = 0⇔x=0
ii) N(xy) = N(x)N(y)
iii) N(x) =1⇔ x is a unit
iv) N(x) is prime ⇒x is irreducible in Z[√d ] .
b) Prove or disprove that C≃ R as fields.
Prove that N:Z[√d]→N∪{0}:N(a+b√d)=|a²-db²| satisfies the following properties for x,y∈Z[√d] :
i) N(x) = 0⇔x=0
ii) N(xy) = N(x)N(y)
iii) N(x) =1⇔ x is a unit
iv) N(x) is prime ⇒x is irreducible in Z[√d ] .
b) Prove or disprove that C≃ R as fields.
-
![Help me with my assignment!]()
Who Can Help Me with My Assignment
There are three certainties in this world: Death, Taxes and Homework Assignments. No matter where you study, and no matter…
-
![How to finish assignment]()
How to Finish Assignments When You Can’t
Crunch time is coming, deadlines need to be met, essays need to be submitted, and tests should be studied for.…
-
![Math Exams Study]()
How to Effectively Study for a Math Test
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
