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Symbol Notation - Intermediate Level: operational symbols INTERMEDIATE

Level up your symbol notation skills with this comprehensive review. 20 intermediate-level problems await in Worksheet 14 of 30. Focus area: operational symbols. Learn logical symbols, notation decoding, symbolic reasoning through systematic practice. Designed for mid-level learners seeking moderate complexity with mixed patterns.

📝 Worksheet 14 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 14 of 30 (46% complete)

Question 1

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

[ 4 8]
[ 2 8]
matrix, advanced

Question 2

If g(x) = x/3, then find g(7)
Substituting x = 7:
7/3 = 2.33
functions, substitution

Question 3

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

Question 4

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: g(f(p(6)))
Evaluate from innermost outward:
g(f(p(6)))
= 25
nested, functions, advanced

Question 5

If ♧ = ×, ∇ = - (standard order of operations applies), then evaluate: 4 ♧ 12 ∇ 8
Substituting symbols: 4 × 12 - 8
Applying order of operations: = 40
arithmetic, basic

Question 6

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

[-1 4]
[-1 -1]
matrix, advanced

Question 7

If P = True, Q = True, and '->' means IMPLIES, then evaluate: P -> Q
Logical operation: IMPLIES
P=True, Q=True → IMPLIES is False only when P=True and Q=False
Result: True
logic, boolean

Question 8

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

Question 9

If P = True, Q = True, and '|' means OR, then evaluate: P | Q
Logical operation: OR
P=True, Q=True → OR gives True if at least one is True
Result: True
logic, boolean

Question 10

If h(x) = x³/2, then find h(5)
Substituting x = 5:
5³/2 = 62.50
functions, substitution

Question 11

If '≽' means '≥', then determine: 11 ≽ 6
≽ = ≥
11 ≥ 6 is True
inequality, comparison

Question 12

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

Question 13

If □ = ÷, ∇ = - (standard order of operations applies), then evaluate: 15 □ 1 ∇ 4
Substituting symbols: 15 ÷ 1 - 4
Applying order of operations: = 11
arithmetic, basic

Question 14

If '≽' means '≥', then determine: 6 ≽ 1
≽ = ≥
6 ≥ 1 is True
inequality, comparison

Question 15

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

[ 8 2]
[10 6]
matrix, advanced

Question 16

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

Question 17

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 18

In the notation system where ☆ means x², what is the value of ☆(7)?
Applying ☆ to 7:
7² = 49
complex, systems

Question 19

If h(x) = x³/2, then find h(1)
Substituting x = 1:
1³/2 = 0.50
functions, substitution

Question 20

If P = False, Q = False, and 'xor' means XOR, then evaluate: P xor Q
Logical operation: XOR
P=False, Q=False → XOR is True when inputs differ
Result: False
logic, boolean
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