Mathematics Exam > Mathematics Questions > Solution set of x = 3 (mod 7), p ∈ Z, is...
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Solution set of x = 3 (mod 7), p ∈ Z, is given by
- a){3}
- b){7 p - 3 ; p ∈ Z}
- c){7p + 3 :p ∈ Z}
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Solution set of x = 3 (mod 7), p ∈ Z, is given bya){3}b){7 p - 3 ...
We first find R-1 we have
R-1 = {(5,4); (4 ,1 ); (6 ,4 ); (6 ,7 ); (7,3}.
We now obtain the elements of R-1 OR we first pick the elements of R and then of R-1 Since, (4, 5) ∈ R and
R-1 = {(5,4); (4 ,1 ); (6 ,4 ); (6 ,7 ); (7,3}.
We now obtain the elements of R-1 OR we first pick the elements of R and then of R-1 Since, (4, 5) ∈ R and
Most Upvoted Answer
Solution set of x = 3 (mod 7), p ∈ Z, is given bya){3}b){7 p - 3 ...
Understanding Modular Arithmetic
Modular arithmetic involves calculations where numbers "wrap around" upon reaching a certain value, known as the modulus. When we say x = 3 (mod 7), it means that when x is divided by 7, the remainder is 3.
Solution Set Explanation
To find the solution set for the equation x = 3 (mod 7), we want all integers x that satisfy this condition.
General Form of the Solution
The general solution for x = a (mod n) can be expressed as:
- x = n * k + a, where k is any integer.
In this case:
- n = 7
- a = 3
Thus, the equation becomes:
- x = 7p + 3, where p is any integer (p ∈ Z).
Why Option C is Correct
By substituting different integer values for p:
- If p = 0, x = 3.
- If p = 1, x = 10.
- If p = -1, x = -4.
These results demonstrate that the set {7p + 3 : p ∈ Z} provides all possible solutions.
Other Options Analysis
- Option A {3} only includes one solution and is incomplete.
- Option B {7p - 3 ; p ∈ Z} would yield values that do not satisfy the original equation.
- Option D (None of these) is incorrect as we have a valid solution in Option C.
Conclusion
Therefore, the solution set for the equation x = 3 (mod 7) is indeed correctly represented by the option {7p + 3 : p ∈ Z}.
Modular arithmetic involves calculations where numbers "wrap around" upon reaching a certain value, known as the modulus. When we say x = 3 (mod 7), it means that when x is divided by 7, the remainder is 3.
Solution Set Explanation
To find the solution set for the equation x = 3 (mod 7), we want all integers x that satisfy this condition.
General Form of the Solution
The general solution for x = a (mod n) can be expressed as:
- x = n * k + a, where k is any integer.
In this case:
- n = 7
- a = 3
Thus, the equation becomes:
- x = 7p + 3, where p is any integer (p ∈ Z).
Why Option C is Correct
By substituting different integer values for p:
- If p = 0, x = 3.
- If p = 1, x = 10.
- If p = -1, x = -4.
These results demonstrate that the set {7p + 3 : p ∈ Z} provides all possible solutions.
Other Options Analysis
- Option A {3} only includes one solution and is incomplete.
- Option B {7p - 3 ; p ∈ Z} would yield values that do not satisfy the original equation.
- Option D (None of these) is incorrect as we have a valid solution in Option C.
Conclusion
Therefore, the solution set for the equation x = 3 (mod 7) is indeed correctly represented by the option {7p + 3 : p ∈ Z}.
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Community Answer
Solution set of x = 3 (mod 7), p ∈ Z, is given bya){3}b){7 p - 3 ...
We first find R-1 we have
R-1 = {(5,4); (4 ,1 ); (6 ,4 ); (6 ,7 ); (7,3}.
We now obtain the elements of R-1 OR we first pick the elements of R and then of R-1 Since, (4, 5) ∈ R and
R-1 = {(5,4); (4 ,1 ); (6 ,4 ); (6 ,7 ); (7,3}.
We now obtain the elements of R-1 OR we first pick the elements of R and then of R-1 Since, (4, 5) ∈ R and
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Solution set of x = 3 (mod 7), p ∈ Z, is given bya){3}b){7 p - 3 ; p ∈ Z}c){7p +3 :p ∈ Z}d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Solution set of x = 3 (mod 7), p ∈ Z, is given bya){3}b){7 p - 3 ; p ∈ Z}c){7p +3 :p ∈ Z}d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution set of x = 3 (mod 7), p ∈ Z, is given bya){3}b){7 p - 3 ; p ∈ Z}c){7p +3 :p ∈ Z}d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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