ReasoningAbility.com

Symbol Notation - Advanced Level: symbolic reasoning ADVANCED

Level up your symbol notation skills with this challenging mix. 20 advanced-level problems await in Worksheet 24 of 30. Focus area: symbolic reasoning. Learn symbol interpretation, symbolic representation, notation systems through systematic practice. Designed for advanced learners seeking complex scenarios and multi-step problems.

📝 Worksheet 24 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 24 of 30 (80% complete)

Question 1

In the notation system where ★ means 2x², what is the value of ★(2)?
Applying ★ to 2:
22² = 484
complex, systems

Question 2

If f(x) = 2x + 1, then find f(6)
Substituting x = 6:
26 + 1 = 27
functions, substitution

Question 3

If ∆ = +, ∇ = - (standard order of operations applies), then evaluate: 4 ∆ 1 ∇ 9
Substituting symbols: 4 + 1 - 9
Applying order of operations: = -4
arithmetic, basic

Question 4

Given: A = {3, 4, 5, 6, 9, 10} B = {1, 4, 6, 7, 10} C = {2, 5, 7} Find: A △ B
Symmetric Difference of A and B:
{3, 4, 5, 6, 9, 10} △ {1, 4, 6, 7, 10} = {1, 3, 5, 7, 9}
sets, operations

Question 5

If k(x) = x - 8, then find k(7)
Substituting x = 7:
7 - 8 = -1
functions, substitution

Question 6

If ⊕ = +, ♤ = - (standard order of operations applies), then evaluate: 6 ⊕ 15 ♤ 2
Substituting symbols: 6 + 15 - 2
Applying order of operations: = 19
arithmetic, basic

Question 7

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

Question 8

Given: A = {2, 4, 6, 9} B = {1, 2, 3, 5, 7, 10} C = {4, 6, 8, 10} Find: A ∪ B
Union of A and B:
{2, 4, 6, 9} ∪ {1, 2, 3, 5, 7, 10} = {1, 2, 3, 4, 5, 6, 7, 9, 10}
sets, operations

Question 9

If g(x) = x + 5, then find g(5)
Substituting x = 5:
5 + 5 = 10
functions, substitution

Question 10

If '≼' means '≤', then determine: 8 ≼ 4
≼ = ≤
8 ≤ 4 is False
inequality, comparison

Question 11

Given: A = {3, 8, 10} B = {2, 3, 6} C = {1, 2, 5, 9, 10} Find: C ∩ B
Intersection of C and B:
{1, 2, 5, 9, 10} ∩ {2, 3, 6} = {2}
sets, operations

Question 12

Given matrices: A = [ 1 5] [ 3 4] B = [ 1 4] [ 5 1] Compute: A + B
Matrix addition:
A + B =

[ 2 9]
[ 8 5]
matrix, advanced

Question 13

If ☆ = -, ◆ = × (standard order of operations applies), then evaluate: 15 ☆ 9 ◆ 3
Substituting symbols: 15 - 9 × 3
Applying order of operations: = -12
arithmetic, basic

Question 14

If '≺' means '<', then determine: 1 ≺ 19
≺ = <
1 < 19 is True
inequality, comparison

Question 15

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(p(5)))
Evaluate from innermost outward:
f(r(p(5)))
= 33
nested, functions, advanced

Question 16

If ♡ = ÷, ◊ = × (standard order of operations applies), then evaluate: 11 ♡ 4 ◊ 12
Substituting symbols: 11 ÷ 4 × 12
Applying order of operations: = 0
arithmetic, basic

Question 17

Given: A = {4, 6, 8, 9, 10} B = {1, 8, 10} C = {1, 2, 3, 5, 8, 9} Find: C − B
Difference of C and B:
{1, 2, 3, 5, 8, 9} − {1, 8, 10} = {2, 3, 5, 9}
sets, operations

Question 18

If g(x) = 3x - 1, then find g(6)
Substituting x = 6:
36 - 1 = 35
functions, substitution

Question 19

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

Question 20

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(4))
Evaluate from innermost outward:
r(h(4))
= 315
nested, functions, advanced
Previous Worksheet Next Worksheet