Activity -3 | Class 12 | Maths

Main Ideas / Concepts Conveyeed

• Topic: “Activity 3” from Class 12 Maths focused on demonstrating functions—specifically how to determine whether a relation is:
  • a function, and
  • one-to-one and/or onto (surjective).
• Sets used:
  • Domain set (M): contains elements {1, 2, 3, 4} (represented using nails).
  • Codomain set (N): contains elements {P, Q, R, S} (represented by other nails/markers).
• Method of visualization: A mapping diagram is drawn using string connections between elements of the left set and the right set.

Method / Instructions Shown

Materials

• White paper / chart paper
• Nails
• String
• Two “sets” of points drawn/placed on the paper (left and right)

Construction Steps

1. Draw or prepare two rows/sets of points on a sheet:
   • Left side (Set M): place nails for 1, 2, 3, 4.
   • Right side (Set N): place nails for P, Q, R, S.
2. Use string to create connections:
   • Join each left element (e.g., 1, 2, 3, 4) to the corresponding right element(s).
   • Each string connection represents the image of a domain element in the codomain.
3. Observe the mapping pattern:
   • For each element in Set M, check how many right-side elements it connects to.
   • For each element in Set N, check whether it is connected to by at least one left element.

How to Decide if It Is a Function

• It is a function if each element in Set M has exactly one image in Set N.
• It is not a function if any element in Set M has two different images (i.e., it connects to multiple right-side elements).

One-to-One vs Onto (Surjective)

• Not one-to-one: occurs when different domain elements map to the same codomain element, meaning images are not unique.
• Onto (surjective): occurs when no codomain element is unused—i.e., every element in Set N is an image of at least one element in Set M.

Key Examples / Mapping Behavior

• Valid function case:
  • Each of 1, 2, 3, 4 maps to a single right-side element.
  • Even if multiple domain elements share the same image, it can still be a function (the key rule is: each domain element has exactly one image).
• Invalid (not a function) case:
  • A domain element (described as something like “3” or “2” in the narration) connects to more than one right-side element.
  • This “splitting” means the relation fails the function rule.
• Onto check:
  • If all elements on the right side (P, Q, R, S) are connected to by at least one left element, the mapping is onto.
  • If any right-side element is never connected, the mapping is not onto.

Lesson / Conclusion

The activity demonstrates:

• how to build a mapping diagram using sets M and N, and
• how to verify:
  • the function condition (exactly one image per domain element),
  • one-to-one and onto (surjective) behavior via the connection pattern.

Final takeaway: The shown relation demonstrates a case of a function that is not one-to-one (while also being described as onto in the activity’s setup). It also explains that a function fails when a domain element maps to multiple images.

Speakers / Sources Featured

• No clearly identifiable speaker name is confirmed.
• Names “Arun” and “Himesh” appear in the narration, but their roles (speaker/students/example) are not clearly confirmed.
• Source: An instructional YouTube math lesson titled “Activity -3 | Class 12 | Maths” (no external sources cited in the subtitles).