How to check whether one number range from one file is the subset of other number range from other file?

I'm trying to find out whether range1 numbers [both columns a and b] are the subset or lying between range2's columns [both columns b and c].

range1

 a       b15       20 8       1037       4432       37

range2

 a       b       c    chr1    6       12    chr2    13      21    chr3    31      35    chr4    36      45

output:

    a       b       cchr1    6       12       8       10chr2    13      21       15      20chr4    36      45       37      44

I have tried to learn from this code [which is working if we wanted to check if a single number is lying in a specific range], therefore I tried modifying the same for two both numbers. But did not work, I'm feeling I'm not able to read the second file properly.

I wanted to compare range1[a] with range2[b] and range1[b] with range2[c]. One to all comparison.

For example in the first run: the first row of range-1 with all other rows of range-2. But range1[a] should be compared only with range2[b] and similarly, range1[b] should be compared only with range2[c]. Based on this only I have written a criteria :

lbs[i] && lbsf1[j] <= ubs[i] && ubsf1[j] >= lbs[i] && ubsf1[j] <= ubs[i]r1[a] r2[b] r1[b] r2[c]15 > 6      20 < 12     False15 > 13     20 < 21     True15 > 31     20 < 35     False15 > 36     20 < 45     False 

Code: [reference but little modified]

    #!/bin/bashawk -F'\t''# 1st pass (fileB): read the lower and upper range boundsFNR==NR { lbs[++count] = $2+0; ubs[count] = $3+0; next }# 2nd pass (fileA): check each line against all ranges.{ lbsf1[++countf1] = $1+0; ubsf1[countf1] = $2+0; next }{        for(i=1;i<=count;++i)                {                        for(j=1;j<=countf1;++j)                        if (lbsf1[j] >= lbs[i] && lbsf1[j] <= ubs[i] && ubsf1[j] >= lbs[i] && ubsf1[j] <= ubs[i])                                { print lbs[i]"\t"ubs[i]"\t"lbsf1[j]"\t"ubsf1[j] ; next }                }}' range2 range1

Thank you.