Explanation

• A cyclic group is a group that can be generated by a single element, i.e., every element in the group can be expressed as a power of that element.
• Cyclic groups are always Abelian, meaning that the group operation is commutative (i.e., the order of elements does not matter).

Explanation

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ND9-11-2022

Explanation

Entropy can be described as the degree of disorder.

Explanation

LCM: Least common multiple

Explanation

Explanation

The possible subsets are ϕ,{0},{1},{0,1}.

ND5-07-2023

Explanation

The distributive law for sets states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

Explanation

To find the largest number that divides 237, 132, and 62 leaving the same remainder, we need to find the differences between the numbers:

237 - 132 = 105

237 - 62 = 175

132 - 62 = 70

Now, let's find the greatest common divisor (GCD) of 105, 175, and 70:

GCD(105, 175) = 35

GCD(35, 70) = 35

The largest number that divides the given numbers leaving the same remainder is 35.

Explanation

In the number 458.21:

The 8 is in the tens place (second digit from the right before the decimal).

Place values from left to right:

4 = hundreds, 5 = ones, 8 = tens

So, 8 represents 80, which is 8 tens.

Explanation

To convert the binary number $11000111$to decimal:

1. Write down the binary number: $11000111$
   
2. Identify each bit's position from right to left: $2^0,2^1,2^2,2^3,2^4,2^5,2^6$
3. Assign the binary digits to their respective positions: $1<font\; color="\#0000ff">,</font>\mathrm{<font\; color="\#0000ff">1</font>}<font\; color="\#0000ff">,</font>\mathrm{<font\; color="\#0000ff">0</font>}<font\; color="\#0000ff">,</font>\mathrm{<font\; color="\#0000ff">0</font>}<font\; color="\#0000ff">,</font>\mathrm{<font\; color="\#0000ff">0</font>}<font\; color="\#0000ff">,</font>\mathrm{<font\; color="\#0000ff">1</font>}<font\; color="\#0000ff">,</font>\mathrm{<font\; color="\#0000ff">1</font>}$
   

Now, calculate the decimal value:

$1\times 2^6+1\times 2^5+0\times 2^4+0\times 2^3+0\times 2^2+1\times 2^1+1\times 2^0$

$=64+32+0+0+0+2+1$

$=99$

So, the decimal value of $11000111$ is $99$

Therefore, the correct answer for the MCQ would be: $$99.