Edunes Online Education
Class 11 | CBSE | MATHEMATICS
SETS | EXERCISE 1.4
📌 1.6 Subsets
A set A is called a subset of a set B if every element of A is also an element of B.
Symbol: A ⊆ B
Example: {1, 2} ⊆ {1, 2, 3}
Example: {1, 2} ⊆ {1, 2, 3}
🧠 Neural Shortcut:
If nothing in A feels “outside” B → your brain tags it as ⊆
If nothing in A feels “outside” B → your brain tags it as ⊆
📌 1.6.1 Subsets of the Set of Real Numbers (R)
The set of real numbers R contains all rational and irrational numbers. Many important sets in mathematics are subsets of R.
Natural Numbers ⊆ Integers ⊆ Rational Numbers ⊆ R
🧠 Brain Ladder Effect:
Visualize numbers climbing a ladder upward into R.
This hierarchical image strengthens long-term recall.
Visualize numbers climbing a ladder upward into R.
This hierarchical image strengthens long-term recall.
📌 1.6.2 Intervals as Subsets of R
An interval is a set of real numbers lying between two given numbers.
Open Interval: (a, b)
Closed Interval: [a, b]
Semi-open: (a, b] or [a, b)
Closed Interval: [a, b]
Semi-open: (a, b] or [a, b)
🧠 Visual Trigger:
Round bracket = exclude
Square bracket = include
The brain remembers shapes faster than symbols.
Round bracket = exclude
Square bracket = include
The brain remembers shapes faster than symbols.
📌 1.7 Universal Set
The Universal Set is the set which contains all objects under discussion. It is usually denoted by U.
If numbers less than 10 are discussed:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
🧠 Neural Boundary Rule:
The universal set acts like the mental boundary box.
Everything else must stay inside it.
The universal set acts like the mental boundary box.
Everything else must stay inside it.
⚡ 30-Second Brain Lock (Exam Hall)
• Subset → All inside
• Real numbers → Biggest number family
• Interval → Between two numbers
• Universal set → The outermost box
🧠 When ideas are stored as spatial images, recall speed doubles under exam pressure.