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Symbol Notation - Advanced Level: coding symbols ADVANCED

Quick competitive exam prep session: 20 advanced-level symbol notation questions. Worksheet 27 of 30 - Focus: coding symbols. Practice symbol relationships, logical symbols, notation decoding with instant feedback. Great for advanced students needing complex scenarios and multi-step problems practice.

📝 Worksheet 27 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 27 of 30 (90% complete)

Question 1

Given: A = {2, 3, 6} B = {2, 3, 4, 6, 7} C = {1, 2, 7} Find: C ∪ B
Union of C and B:
{1, 2, 7} ∪ {2, 3, 4, 6, 7} = {1, 2, 3, 4, 6, 7}
sets, operations

Question 2

If '≻' means '>', then determine: 7 ≻ 14
≻ = >
7 > 14 is False
inequality, comparison

Question 3

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: h(g(4))
Evaluate from innermost outward:
h(g(4))
= 576
nested, functions, advanced

Question 4

Given: A = {5, 7, 10} B = {2, 6, 7, 8} C = {2, 6, 7, 8, 10} Find: B − C
Difference of B and C:
{2, 6, 7, 8} − {2, 6, 7, 8, 10} = {}
sets, operations

Question 5

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: r(h(3))
Evaluate from innermost outward:
r(h(3))
= 38
nested, functions, advanced

Question 6

If P = False and '!' means NOT, then evaluate: !P
Logical operation: NOT
P=False → NOT flips the value
Result: True
logic, boolean

Question 7

Given: A = {2, 4, 5, 7, 10} B = {1, 3, 5, 6, 7, 10} C = {2, 3, 5, 7, 8, 10} Find: A ∩ B
Intersection of A and B:
{2, 4, 5, 7, 10} ∩ {1, 3, 5, 6, 7, 10} = {5, 7, 10}
sets, operations

Question 8

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: f(r(g(6)))
Evaluate from innermost outward:
f(r(g(6)))
= 327
nested, functions, advanced

Question 9

If ☆ = -, ⊗ = × (standard order of operations applies), then evaluate: 8 ☆ 14 ⊗ 2
Substituting symbols: 8 - 14 × 2
Applying order of operations: = -20
arithmetic, basic

Question 10

If '≠' means '≠', then determine: 10 ≠ 19
≠ = ≠
10 ≠ 19 is True
inequality, comparison

Question 11

If P = True, Q = True, and '<->' means IFF, then evaluate: P <-> Q
Logical operation: IFF
P=True, Q=True → IFF is True when both are same
Result: True
logic, boolean

Question 12

In the notation system where ▼ means x² - 1, what is the value of ▼(2)?
Applying ▼ to 2:
2² - 1 = 3
complex, systems

Question 13

Given matrices: A = [ 5 4] [ 3 2] B = [ 2 2] [ 4 1] Compute: A - B
Matrix subtraction:
A - B =

[ 3 2]
[-1 1]
matrix, advanced

Question 14

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: f(r(6))
Evaluate from innermost outward:
f(r(6))
= 37
nested, functions, advanced

Question 15

If ⊖ = -, □ = ÷ (standard order of operations applies), then evaluate: 9 ⊖ 2 □ 9
Substituting symbols: 9 - 2 ÷ 9
Applying order of operations: = 9
arithmetic, basic

Question 16

Given matrices: A = [ 3 2] [ 2 3] B = [ 4 3] [ 5 2] Compute: A + B
Matrix addition:
A + B =

[ 7 5]
[ 7 5]
matrix, advanced

Question 17

In the notation system where ♣ means x/2, what is the value of ♣(7)?
Applying ♣ to 7:
7/2 = 3.50
complex, systems

Question 18

If P = True, Q = False, and 'nand' means NAND, then evaluate: P nand Q
Logical operation: NAND
P=True, Q=False → NAND is True except when both are True
Result: True
logic, boolean

Question 19

If h(x) = x - x/2, then find h(10)
Substituting x = 10:
10 - 10/2 = 5
functions, substitution

Question 20

If P = False, Q = False, and '<->' means IFF, then evaluate: P <-> Q
Logical operation: IFF
P=False, Q=False → IFF is True when both are same
Result: True
logic, boolean
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